There’s a couple of issues that aren’t being separated here.
Are there instances of exotic big cats that escape from captivity? Yes. Is this common? No.
Do escaped exotic big cats form breeding populations? Almost certainly not, because big cat escapes are pretty rare. And in many places we already have native species of big cats. North America has lynx, bobcat, cougar, and (extreeeeeemly rarely north of the Rio Grande) jaguars. In North America if the area would support a breeding population of escaped exotic cats it probably already has a breeding population of native cats. Obviously, this isn’t the case in the UK or Australia, but the UK doesn’t exactly have a lot of wild area, and how many exotic big cats go missing in Australia?
Do those exotic big cats interbreed with feral domestic cats? Almost certainly not. This isn’t a case of wolves interbreeding with dogs. The european/african wildcat is the wild ancestor of domestic cats. Wildcats do interbreed with domestic cats because they’re the same species. But wildcats are about the same size as domestic cats. A european wildcat looks like an extra-tough extra-mean tabby. File:Wildkatze 002.jpg - Wikipedia. Note that that image shows two cats, you just can’t see the head of one. Or this image: http://www.fow.org.uk/WP_Wildcat.htm. This is the kind of cat feral domestic cats would be interbreeding with, and wildcats are about 3 to 6 kg, the same size range as domestic cats, not bigger. Yes, domestic cats will hybridize with exotic species, but this happens only in captivity. And domestic cats won’t hybridize with species that are much larger than domestic cats.
Are domestic cats sometimes really large? Sure, for varying definitions of “large”. Some domestic cats like Maine Coon Cats are startlingly large, although long fur can make a cat appear larger than it really is. And cats can be both larger and smaller than people expect…a cat can squeeze themselves into a tiny ball or through a tiny opening, yet stretch out amazingly long.
Are eyewitness reports of really large domestic cats generally accurate? No! How do the eyewitnesses get a sense of the scale of the animal? To give a silly example, my home office window looks out at some forestland. The other day someone was walking past my window through the trees and they looked tiny…until I realized that my day to day perception of how far away the trees were and how large the trees were was inaccurate. The trees were larger and farther away than I thought, so when a person walked by them I percieved the person to be smaller than they really were…for a second or two, then my brain readjusted and the trees got bigger. Anyway, the point is that simply seeing an animal far away…especially if you’re looking at them through a scope or binoculars…is bound to give you an inaccurate estimate of the size of the animal.
And do people deliberately fake photos of cats to make them appear larger and smaller than they really are? Of course. Every single one of the dead cat photos I’ve seen was arranged in such a way as to deliberately give a false impression of how big the cat was, when it would be easy to take a photo in such a way as to give a reliable sense of scale.