First off, thanks to the OP for exemplifying what I believe to be a mutual respect between Bama and UT fans. It is nice to hear a little reflection on the pedigree of our new coach.
Second, I think that the argument over having another fanbase congratulate you on a hire (or vice versa) somehow reflects on their lack of fear (or vice versa) is absurd. We see how Kiffin beat up on our rivals after hearing all the negativity from other fans, right? There is some element of respect and class that exists in long-time fans, and some of us just like to see good football. It's understandable that Bama hated Fulmer, given the legal history. I actually think this hire might be very, very good for our storied rivalry.
Finally, as to Bama fans: I have never been sorely mistreated by a Crimson-faithful. My last trip to T-town (albeit an embarrassing one) was quite enjoyable, and we always enjoy the Tide following in Knoxville. Florida? Georgia? Auburn? Not so much. But "old money" is "old money," and we share a mutual respect.