Some of them don't know that, and there have been more than a few accounts from people on this forum where they were told by less informed LEOs that they would arrest anyone who had any alcohol in their system while carrying.
I've been issued an 80mph in a 60mph zone by DPS while my speedometer read 65mph (right as you're coming into Waco headed north, just after it drops to 60mph from 65mph). I was really confused as to why I was pulled over and only found out that it was for speeding after the trooper brought me my ticket. A quick call to the judge's office is all it took to discover they would dismiss it if I got my speedometer "fixed" (a receipt from any car shop would suffice, in my case). It wouldn't hurt to call and ask.
All in all, I think your stop went waaaaaay better than it could have.