No that's wrong. Harry suggested that he use Pigwidgeon instead and that's what made Hedwig oblige. Trust me, I was reading that portion over and over just yesterday because I didn't truly understand why Pigwidgeon would nip Harry "Harder the usual" because he's never really had any contact with him.
what chapter is that in?? they send Hedwig out twice, then Sirrius says to change owls, so they send a school owl because Ron is still mad a Harry, then they send Pig, and then they don't send owls any more. maybe I missed it. oh yeah and Hedwig is a girl, secret_cockrel.
OK, Harry sent his reply back to Ron about the quidditch world cup through pig. He then asks Hedwig if he's up for a long flight and after an answering hoot attaches his letter to Sirius on Hedwig's leg and watches him fly out of the window. This is not a slipup.