Full-disk encryption is primarily used to protect offline volumes. If no one can boot your disk, it doesn't matter if Microsoft can upload its entire contents to the NSA once Windows is started. The concern is that a flaw in BitLocker's FDE would make it vulnerable to attacks while the volume is offline.
FDE doesn't really protect online volumes. Yes, the disk is still encrypted, but the OS transparently decrypts any requested sector, so other security measures are necessary to protect mounted volumes.
1. RSA released software with backdoors, at the behest of the NSA.
2. Therefore, the NSA has the ability to make companies release software with backdoors.
3. The FBI and British governments are known to have asked for backdoors to be included in BitLocker.
4. Therefore, the NSA has the motive to have a backdoor put in.
5. Microsoft have not proved BitLocker /does not/ contain backdoors.