I think there might be an explanation in store in future movies. The year 1935 is never mentioned anywhere "official", neither on pottermore nor in the "Short stories from Hogwarts" ebook, where her life story is told. it only ever says "4th October".
The reason so many people believe she was born in 1935 is because when asked by Umbridge in book 5 how long she has worked at Hogwarts, she says "this december it will be 39 years". From there, using the information we have about her life and when she started, the year 1935 can be calculated for her bith.
Meaning, this 1935 date relies entirely on the assumption that Minerva told Umbridge the truth!
The scene where she talks to Umbridge is the ONLY clue we ever got to her actual age. If we assume that she lied, it's totally plausible for her to have been alive and teaching in 1927. She'd still be younger than Dumbledore, so it's not far-fetched to assume she'd still be around in the 90s.
It might just have been a mistake of course, but i personally still have a bit of faith that there's a good explanation to all of this, and that we might even get a reason that would make her lie to Umbridge later (though she might just have done it because she hated her).