It's true that a tire engineer designed those two tires to work in tandem, so he can safely make an engineering judgement that those two tires are the optimum combination based on the parameters of his test, because those two tires were tested together. That allows the legal department of the tire company to say that the manufacturer recommends that only matching tires be used, and they won't recommend that mismatched tires be on the bike. Mainly because they've only tested those two tires together, and not every possible combination of tires. From both a legal and engineering standpoint, they're protected. There's no upside to a tire company trying to test every other tire on the market, or even other tires within their own brand, to say that this brand will work with that brand. If you notice, engineers don't say it's inherently dangerous to mix tire brands; only that it isn't recommended (because they aren't going to recommend something they didn't test).
So what you're left with is anecdotal evidence from other guys who've mixed tire brands; since no engineer will ever test them, anecdotal evidence is the best evidence you're going to get. I can say that I have mixed a front Battlewing 501 with a rear Shinko 705 with no issues, under the conditions of how I ride (I'm a pretty low key rider). If I was the kind of rider that pushed my bike to the extreme all the time, I would probably not mix tires; if I was constantly at the edge of the performance envelope, I'd opt for the absolute best combination of tires. For me, the Battlewing and Shinko were a good combination; good wet performance, decent tire life, good cornering, and a lot less vibration than a Shinko front/Shinko rear setup. I ran the Battlewing on the front through two different 705 rears, until the BW wore out; then I replaced it with a Shinko (because the Shinko was cheaper).
I don't think anyone can honestly say that any front tire is a good match with any rear tire; tires do behave differently, and do have differing levels of performance in things like wet environments. It's probably as unsubstantiated to say that every mismatched tire combination is fine as it is to say that no mismatched combination is fine.
"No matter where you go, there you are."