You cut out 2 seconds of it. You could argue that that's an entirely different song.

You could, but the court would still say no. Part of the copyright law states that even copying a portion of a work still constitutes copyright infringement.

... they could say singing it or playing the song on an instrument is illegal...

Not really. Reproducing the work in a new form (singing isn't exact reproduction, unless you're really damn good) can fall under Fair Use as it affects how much origial content is taken.

Copyright law is a gray area, and is always subject to the exact circumstances of the case. It's not just the action, but the motivation, and the extent of the copying that determines if it's really illegal.