Can a basketball legally hit the top of the backboard?

It is not legal under NCAA rules:

Art. 3. The ball shall be out of bounds when it passes over the backboard

from any direction.

In NBA the rule is slightly different:

b. Any ball that rebounds or passes directly behind the backboard, in either direction, from any point is considered out-of-bounds.

Note the Word 'directly'. Here's the official interpretation from NBA vice president of referee operations Joe Borgia in 2009:

"Think of the backboard as a long tunnel that goes straight back," Borgia said. "If the ball goes through that tunnel, it's a violation. If you looked at Rondo's shot, it was an arching shot up and over the backboard. It never passes through the tunnel."

This is why Bird's shot is waived off while other shots that flew over the backboard but not from behind the backboard are valid.

Bird's shot is legal under FIBA rules.