I've never heard of that being true (that doesn't mean it isn't), but one program using both protocols won't make it any worse, since in all likelihood all computers on a network are using both anyway. That article talks about TCP and UDP being used at the same time, but not by the same program or even computer. Its talking about using them at the same time in the same network. If you really want to avoid packet loss, then you shouldn't run any web browsers when playing games on any computer on your network.
And honestly, if many multiplayer games use both and don't have problems, then it won't be a problem except for the fact that it does complicate things.
I believe Source engine uses both TCP and UDP (TF2, L4D, L4D2, CS:S, Portal 2 Co-op, Garry's Mod, and a bunch more).