It appears that you are asking your question from the perspective of halachic curiosity and do not have plans to demand your money back. Thus, we do not have to be as rigorous as we normally would be in considering all relevant issues, some of which may be unknown to us since we are hearing from only one side. Your excellent question has an interesting provisional answer.
The gemara[1] tells of one who took a vessel from its maker to check it and keep it if he liked it. Shmuel says that even if something happened to the vessel b’oness (by no fault of his own), he is still obligated to pay. This is how the Shulchan Aruch[2] rules in a case in which the parties had decided on a price and the seller was not particularly anxious to get rid of the object.
In your case, it would ostensibly seem that you would be similarly obligated to pay. However, the point of meita machamat melacha is a good one. Even a sho’el, who is obligated to pay even when something went awry b’oness, is nevertheless exempt if the object died, broke, etc. as a result of being used in a normal manner,[3] and a string breaking while tuning the cello seems to belong in this category.
However, we must understand the halachic mechanism that normally obligates the provisional buyer. The Rash[4] explains that since the buyer is in the advantageous position of being able to buy or to return the object as he likes, Halacha places upon him the broad responsibilities of a sho’el, who also has the main benefit from his arrangement. Rashi[5] says that the logic of the obligation is that the tentative sale makes the receiver of the object considered to be a buyer (lokei’ach), even if he has the ability to return it. When one buys an object and something happens to it after the sale is complete, the loss naturally is his. The Netivot HaMishpat[6] maintains that actually both possibilities (sho’el and lokei’ach) exist, and which mechanism is the one that has impact depends on the particular circumstances.
There are practical halachic differences between the approaches. The Machaneh Ephrayim[7] discusses one such difference: when the seller was working for the buyer at the time of the sale. This situation, when discussed in the laws of watchmen and particularly those of a sho’el, is called b’alav imo (literally, the owner is with him), and the Torah grants the sho’el a special exemption from payment in that case.[8] Thus, if the provisional buyer’s obligation is due to a status of sho’el, the exemption of b’alav imo will apply. If the obligation is based on lokei’ach, then b’alav imo will make no difference, as we are not obligating the buyer to pay for what happened to the object but are just saying that once he bought it, any loss is naturally going to affect him.
Our case seems to be another one in which the halacha would depend upon the conceptual basis for the potential buyer’s financial obligation. Meita machamat melacha is also a special exemption for a sho’el, as we noted above, but similar to b’alav imo, we do not expect it to provide relief for one who is considered a lokei’ach. Since the majority opinion is that a provisional buyer is a lokei’ach[9] (and according to the Netivot HaMishpat,[10] both types of obligation apply), you seem to have been obligated regardless of the fact that the cello broke in the course of its normal use.
However, one might be able to distinguish based on the following. How can one be considered a lokei’ach if he can exercise his right to back out of the sale? The Tur[11] implies that the condition is that he can back out if he returns the object intact. Regarding a classic damage, like a theft or an animal dying, which are total losses, there is no way to back out of the deal. Consequently, the purchase remains intact and the potential buyer turns into an actual one and is stuck with the worthless object. However, since you were able to return the cello with only minor damage, the seller could obligate you only through the rules of sho’el, by which you were exempt due to meita machamat melacha.
If you were to make that argument for an exemption in a beit din, you would apparently need to prove that the breaking of the string was a result of meita machamat melacha, i.e., that it occurred during normal use without fault, or swear that this was the case.[12] Because of the difficulty of doing so and since we cannot assure you that the above halachic analysis fits your exact case, reaching a compromise is a reasonable solution. Certainly, it would be difficult for you to legally force the seller to return a payment you already made.