I should have known better. I know that in an oxidation-reduction, there must be a transfer of electrons. When I went searching through some texts, I found that Zumdahl's "World of Chemistry" states that, "In fact, we can think of these synthesis reactions as another subclass of the oxidation-reduction class of reactions." But the examples that were discussed here all involved the transfer of electrons. The idea that synthesis could be anything but a redox is not even mentioned - which is probably where I got the idea in my head that it had to be a redox.
Thanks!