It must be a stray because it's not a pedigree cat
I just spoke to a woman about a cat running into her flat. It only runs in during the wee hours of the morning and it has been doing so regularly for the last week. She said that there used to be cats running in periodically for the entire time she's lived there (the last twenty years) but it's gotten a lot worse lately.
I explained that cats rarely run up and that it could be that they only go in during that time because they may be let out when the owners are asleep. It is also possible that they go in during that time because it's quiet. I explained that usually when cats go up, they are community cats being lured up by someone or cats that are pets let out to roam.
She took this all in and suggested one family that might have a cat. However she said she thought the cat was a 'stray' - I asked if it was because it looked especially scruffy, or not well groomed or what made her come to that conclusion. I realised that she meant it wasn't a pedigree. When I explained to her that many people actually do own non-pedigree cats, she sounded surprised. I think it highlighted to me that sometimes people do have misconceptions of cats and that they come to conclusions, not necessarily because they are malicious but that they do not know any different.
She asked for some solutions to help keep the cat out and sounded quite willing to try them. I told her we'd look into the case.