A Hypothetical that (is) WAS Giving Me Trouble

This post is all business, and not in the least entertaining.  It is just a problem I have understanding a Gemara.

Hypothetical, based on a Mishna in Bava Basra:

A and B are partners in a business.  A and B invested in the business, and hired M (Manager) to manage it.  M is paid a salary.  Years pass. B and M die.  The business is liquidated, and it is now worth three thousand dollars more than A and B invested in it.  A, the surviving partner, tells the heirs of B and M that when they began the business, M was promised that besides his salary, he would have an equal share in the equity the business developed.  Therefore, A says, the three thousand dollars should be divided equally among A, the heirs of B, and the heirs of M.  The heirs of B and M have no idea whether this is true or not.

How do you divide the three thousand dollars?

The obvious answer is:
        B is entitled to one thousand five hundred dollars, half the assets, because there is no evidence that shows that M was a partner, and so the only partners, as far as the heirs of B know, are A and B.  Until evidence is produced, B is entitled to half the assets.
        A agrees that he is entitled to no more than that one third, because he says there are three partners.  Therefore, A is entitled to what he claims is his, namely one third of the assets, one thousand dollars.
        M will receive the remainder, five hundred dollars, or one sixth of the assets.
This is indeed the solution stated in the Mishna in Bava Basra 134A.

(I changed the characters from the case in the Mishna, but the idea is the same.  The case the Mishna gives is that the father of A and B died and left an estate to his children.  A says that he knows for a fact that X is also a brother, and so they should each get one third (there is no bechor).  B says he has no idea whether X is a brother or not, and is not interested in giving away a portion of the estate to X until his relationship is proven conclusively.  So B says he wants half of the estate.  X also says he doesn't know for sure whether he's a brother.  The Mishna says that if there were three fields in the estate, B gets one and a half (half the estate), A gets one (one third of the estate), and X gets one half  of  a filed (one sixth of the estate --זה אחי אינו נאמן ויטול עמו בחלקו.)

I don't think this is the right solution.
I think that once B has taken half the assets, A and M should split the remainder.  M's claim is against the assets that remain after B has taken what he thinks is his, not against B.  A agrees that he and M are on an equal footing.  Therefore, A and M should split the remaining assets.  The money wasn't labeled A's, B's, and M's.  It's just anonymous money.  B did not take half of M's share, he took one thousand five hundred dollars.  All that remains is one thousand five hundred.  If A and M are equal, they should divide that remainder.  That is, B takes one thousand five hundred, and A and M each take seven hundred and fifty.  Or, in the case of the Mishnah and the fields, B takes one and a half fields, and A and X take three quarters of a field each.

To make it more clear: if there were three partners, A B and M, and B takes more than a third of the assets because he has a grudge against M.  A knows that B's act is wrong, and that B had no right to do what he did, but nobody can stop B.  He left the country, or he's a tough guy.  What will you do with the remainder of the assets?  Of course, you will divide it equally between A and X.  B's act of theft doesn't change the rules.  Here too, B's taking one and half thousand is, from A's perspective, nothing more than an act of theft.  B might justify it by saying he's entitled to take it.  But A knows that's not true, so it's nothing more than theft from the remainder of the assets.

Maybe my mistake is in assuming that M's claim exists in the form of an ownership of a percentage of the assets.  Maybe partnership interests are not viewed as ownership of assets but are viewed as a quantatative claim against each of the other partners in a percentage determined by the number of partners.  In other words: There are three partners, A B and C.  A's one third holding exists in the form of a claim against B (or B's capital account) for one sixth, and a claim against C for one sixth; B's one third holding is in the form of a claim against A for a sixth and against C for a sixth, and so on.  If that is the case, then here, according to A, M has a claim against A and B for one sixth each, and no more.  So after B has taken his half, including the one sixth that A says M is entitled to from B, his claim against A is still only for one sixth of the assets.

I just don't know why Chazal would assume this Byzantine interpretation to be correct.

I am happy to announce that those of you that thought that my kashe is a TIPSHUS are WRONG.

Not only am I not wrong, but I found that  the    אור שמח in  פי"ב מנז"מ הי"ט asks the kashe, thank you very much Reb Meir Simcha.  In fact, he even asks the kashe the same way I tried to explain it to my wife last night at supper (with a case of shutfim dividing partnership assets after a portion of the assets were stolen.). (The demonstrated fact that my Seichel has not gone haywire may be the biggest chiddush in this post.)
Yes, Reb David Povarsky holds it's not a kashe.  See his shiurim here.  But A., I think he's wrong, and B., right or wrong, I'm quite content to have my seichel hayashar validated by saying something Reb Meir Simcha said.

So what does Reb Meir Simcha say?  He answers

אלא ודאי מוכרח דכיון שהוא יש לו ראיה
ליטול חלקו שהניח אביו שדה שלמה ,
רק החסרון הוא בהאח שבא ממדינת הים
שאינו יכול לברר שהוא אח , וא"כ כיון דמה
דהאח הראשון מחזיק בחלקו שדה ומחצה
הוי מדינא , מצד חסרונו בראיה שאין לו לברר
בב"ד שהוא אח , לכן איהו מפסיד ואין לו
לאחיו השני בזה ההפסד כלום

(Please note that Reb Meir Simcha relabeled the parties: the man he calls "Hu" is A, and the man he calls "Ach Rishon" is B.)

Translation:

(connected to the discussion in Bava Kamma 53 on כל היכא דלא אפשר לאשתלומי מהאי משתלם מהאי:)

It must be that since (known brother A) can prove his right to a whole field (because he's certainly entitled to one field out of the three), and the fault is in the inability of (X) who has come from far away to prove that he is a brother, so the fact that (known brother B) takes his share of one and a half fields is legally supported by the failure of (X) to prove his relationship, so (X) loses and (known brother A) does not have to share in (X's) loss (by allowing X to take half of the one and a half fields that remain after B took his share).

I think that what he's saying is this. Here,   A says to X, you can't take your fair share from B because we can't prove your case.  Until we or  you prove your case, B is really entitled to take the larger share.  Since it is the weakness in your ability to prove your case that results in B's legal right to take the larger share, it's your problem, not mine.

Hakaras hatov: I found the teretz during a search of hebrewbooks.org.  What a wonderful resource that is!     

And, Harav Eli sent me the a pdf from Reb Shmuel Rozovsky on Bava Basra to Daf 134, who says that Rabbeinu Gershom learns pshat in the Gemara as I suggested.  If I can get it from pdf to here, I will, bln.