Sure. XTS reuses the sector-block for an IV, and so on a per-block level encryption is deterministic. The flaw here would be a scenario where there are deliberate repeated modifications to blocks of the harddrive (somewhere like within hibernation/wake code). Something carefully designed could, in theory, lead to the compromise at a block level that would allow tweaking of some contents on the disk (say, contents of the registry, or of some boot switches, etc) that would in turn enable the machine to be booted and the disk to be decrypted.

It's also true that the TPM protector for bitlocker uses a pin with max ~20 bits of entropy to shield the bitlocker key from exfiltration. The TPM is supposed to lock out repeated requests to extract they key but given the heavy involvement of the NSA in designing the TPM spec and its similarity to the Clipper Chip in function (so too with Apple's "Secure Enclave"), and its difficulty to audit (as if mom and pop consumers really need protection from adversaries who are going to reverse TPM chips to get computer data), one can't help but to acknowledge that a backdoor could easily exist there.

All of this is hypothetical of course. I don't claim to know that this sort of attack is there or that it is placed deliberately. I'm merely trying to make the point that a backdoor need not be in the harddisk encryption code itself.