[Bava Kama 19, Rambam Hilchot Nizkei Mamon 2:9]

It seems clear that Maimonides and Tosphot are agree in principle about the case of a hen with a string attached to its leg and a pail gets caught in the string an breaks. It really bothers me to say this but in spite of the fact that the Migdol Oz tries to defend the Rambam by saying he is like Rashi I think it is crystal clear that this can't be true.

You find a movement started by Reb Chaim Solovietckik to try to give answers to the question why does the Rambam decide like he does.
The major personalities in this movement were Reb Chaim himself, Reb Baruch Ber Lebovitz, Reb Shimon Shkop, Rav Elazar Menachem Shach ( of Ponovith in Bnei Brak in the 1980's).
Rav Sach wrote the Achiezer on the Rambam and that was the last of this massive effort to understand the Rambam that I am aware of. 

You can see what I am saying if you read between the lines. When Reb Chaim wants to deal with the Rambam in how he decides the law about something not intended on Shabat he ignores the answer of the Magid Mishna --almost as if to say that it is not worth serious consideration. [Which indeed it is not. I wrote about this elsewhere.]

Here is the basic issue in short.We have a debate between Rabbi Nathan and the sages about the case of a ox pushing another ox into a pit in Bava Kama 53a. To R.Natan what you can't get from the owner of the ox you get from the owner of the pit. In our case in Bava Kama 19a we have a hen with a string attached and a bucket that gets tangled in the string and breaks. To the Rambam when the  string has an owner, he alone pays not the owner of the chicken. Clearly the Rambam holds the difference is when the string has an owner he alone is responsible, and the case of the ox and pit is different because there both owners are responsible. Exactly like Tosphot-- Not like Rashi there who says that even though the owner of the pit pays it is a {kenas} penalty  and not that he is really responsible.
Also let me add something I have mentioned before this. Why if the string has an owner that he alone is obligated" why could not both people be obligated like in the case of R. Natan? Answer because in the case of  a change like flying or a string attached there cant be more that one half damage. This principle you see in Tosphot and the Rambam both. It is the reason Topshot gives for why the Gemara rejected its original approach to Rav Huna. [Not like Rashi!] And this is the only possible reason the Rambam could have to saying the owner of the hen is not responsible in the case when the string has an owner!

It seems to me that there should be some effort to understand the opinion of Maimonides in The Guide for the Perplexed also.