How is it scientifically possible?
Interstellar travel does not require FTL travel. STL travel is entirely practical if aliens either use generation ships, do not age significantly, or some combination of two. We actually already have the technology for interstellar travel, we just do not want to go anywhere bad enough. A nearly immortal species with a more long term view and mature space technology might not have any reason not to travel.
Where do they most probably come from?
Lacking FTL they'd need a nearby base, the hidden side of the moon would probably be most appealing "safe" place to observe humans. Or you can assume they have pacts with national governments that allow them to use bases on Earth.
As for the ultimate origin, I have no guess really. A civilization doing STL exploration could hop from star to star over millennia, even hundreds of millennia. The ultimate home system might well be beyond our current capability to detect Earth-like planets.
And what does make them look so gray?
Lack of pigmentation? Genetically engineered species that spends millennia in spaceships travelling between stars does not really need pigmentation.
Should I simply accept the fact that assumption "aliens do visit us" is wrong and the people claiming to be abducted are simply wrong?
Yes. It is the most reasonable assumption to make. Certainly the vast majority of UFO-theories make no sense or have much more likely origin than actual alien visitors.