^ Singer never said it was a direct sequel. He said it was a loose sequel. Essentially, he picked and chose what he wanted to be consistent with the original movies.
And that was a big part of my problem with the film. It was too half-hearted, stuck between paying homage and doing something new. It lacked a clear identity of its own. I'd rather have seen it commit wholeheartedly to creating a new, fresh take on Superman. That would've been a better tribute to Donner than just copying elements of Donner's films, because it would've instead been following in the footsteps of Donner's approach
: reinventing Superman, bringing a fresh, modern take to it.
I've never had a problem with that sort of approach. I've always taken it when viewing the Bond movies. My interepretation has always been that e.g. Pierce Brosnan's character took on Goldfinger but he didn't make jokes about The Beatles, he made jokes about Take That. He has a history that is vaguely like that of Connery Bond, Moore Bond or Lazenby Bond and Dalton Bond, but in my continuity, he never fought on a space station, a la Moonraker.
I have no problem taking a similar 'pick and choose' approach with Superman. Indeed, I find it hard to understand how those who read comics, with their ever changing continuity and backstory, can't approach movies with the same attitude.