Back on page four iBump 2.0 asked:
at the end of book 1, Dumbledore said that his and Hermione’s owl crossed in mid-air, however a few pages later Hermione says to Harry that that she ran into Dumbledore on the way to the Owlery to send him the owl
The answer is that Dumbledore had indeed returned before Hermione could send an owl. Harry, when questioning Dumbledore, did not know this and assumed that Hermione had actually sent an owl. Dumbledore, therefore, thought that Hermione had sent an owl, and thus assumed that he must have crossed it in midair.