So, if I understand you correctly -- you put your fob under the floor mat for a week and then placed the fob on your person (probably in your pocket) for a few weeks and that seems to have corrected the problem ? Perhaps you are on to something. Maybe a few more people who are having BCM issues will try what you did and we shall see if indeed this is working. Will look forward to see some responses -- be they positive or negative.
I doubt this very much.
As they say, observation is not causation. The BCM interacts with a range of things in the vehicle, and a malfunctioning BCM means no observation of symptoms can be used to conclude cause.
Could simply be the vehicle recognizes the fob is inside the vehicle, which in turn prohibits some features from working (like locking the vehicle doors). A fob inside the vehicle results in the BCM behaving differently than a fob outside the vehicle. But broken is broken, even if you can find some conditional work around you "think" prevents the issue.
We have to be mindful with problems like this that are being discussed by a range of affected owners. They very often result in suggestions of unverifiable work arounds, as well as inaccurate beliefs and comments.. and even sometimes superstition enters the conversation. A read through on the now solved and discussion closed topic from early in gen5 production about abnormal oil rise, demonstrates this well. If you read that thread from front to back (tedious but informative) you will find many ideas, suggestions, prophecies, and claims that were in fact completely wrong, making actual verifiable facts in the discussion hard to glean for the casual forum member.
No harm in trying though.