Could he do that, though?
Actually, I'm looking at the page now...he tries "accio" but it doesn't work. I guess it's like how throughout the book they try "accio" on various objects but it doesn't work because they're protected. This causes Harry to think about the qualities needed to be a Gryffindor...daring, bravery and that's why he dives into a freezing lake. Plus Dumbledore told Snape not to let Harry know that it was he who was giving the sword to Harry, so he had to do something convoluted like this to perhaps make Harry think the sword was coming to him, like it appeared in the Sorting Hat in The Chamber of Secrets.
Damnit, Lenny!
