I have a CD on which there is a song in the key that I would expect. Before I bought the CD, I had the same album on a commercially produced tape cassette. This played the song at something like a quarter of a tone below that expected and was impossible to play along with on any correctly in-tune instrument. Obviously my tape player was running slower than it should have been.

The "Singing in the Rain" example of Ab to E does seem to be rather extreme but perhaps, if it's not too far from the requested key, it could be a problem of reproduction rather than an actual mistake.

DC