This is admittedly a half-baked and "out there" point to consider, and I'm sure it will draw more than its share of "Woo!" responses here, but I wanted to open up this topic for consideration.
If you've not ever encountered the theory of Biocentrism, and its chief proponent, Robert Lanza, I'd encourage you to read up on it. The idea is a fascinating one, and he is right on one of his chief observations, in my opinion: Something about this theory of time/space/perception rings "true" to me. If you've ever tried to wrap your head around quantum theory (especially the duality of matter as particle AND wave forms) this will be right in your wheelhouse. His writings have triggered in my mind a number of thoughts about our favorite crypto-critter that I wanted to lob out there for discussion and consideration.
One thing that has always intrigued me about the sighting reports is a...I don't know..."disconnect?" between the two putative species when we come into close proximity. The reaction/demeanor of the BF has been described many times, or I would characterize it as, disinterested, nonchalant, and even "cool". When you look at the PGF, you can't help but note an overall under-reaction by the subject. Almost as if Patty recognizes "something", but she does not react as I would expect another two-legged creature to react to another one, especially not one encountered unexpectedly. There are many of what I would consider credible encounter reports of the animal looking right at the witness, but giving no noticeable reaction whatsoever until they just turn and walk (and it is almost always at a walk). I've always found this to be a fascinating fact.
Although I completely understand the current lack of ability to confirm/refute this hypothesis, let me just throw out the theory that BF, fundamentally, perceives the world, and us, in a manner that would not only be incomprehensible to us, it also creates an inner-species barrier that prevents them from even perceiving us as we at least think we are to them.
How's that for a problem?
A primer on the theory of biocentrism: