sorry to hear of the problems you are having
it is not common for a BMW transmission to fail at this mileage, especially if it has never had to be serviced or had any problems in the past. BMW transmissions can fail at relatively low mileages (between 100 and 150k miles) but 50k is VERY low for this so there may have been some defect in this particular transmission - or it could just be random bad luck.
If the fluid is burnt and contains filings, then I am afraid their diagnosis does sound correct - this usually points to the need to replace or rebuild the transmission.
If you are out of warranty, then unfortunately BMW has no responsibility. However, you can ask BMW corporate and your dealership for goodwill assistance in covering all or part of the repair.
Sorry if you were hoping for a different answer, please don't shoot the messenger - I can only give the honest answer, which I have. Please remember that a low rating PUNISHES me for my honest and prompt response, and I receive nothing for my time and answer until a positive rating is clicked.Please let me know if you have further questions. Please do not forget to click a positive rating as this is the only way I receive credit for my answer, thank you. Best wishes with your vehicle