Splintered sub floor under kitchen

One comment on the advice you read is that I don't see a thing in there about deflection - evidently Mike Holmes is sure that if he merely has 1-1/4" of subfloor, all is good. Real tile specs tend to involve a concept called deflection, and that's the distance part of the floor system moves when loaded, relative to the span you measure over. L/360 is a typical spec - L/180 is twice as bad. (It's usually a lowercase L, but on the computer I'm using a capital to be clear that it's an L.) I happen to have a 3/4" subfloor that's L/587, so it really doesn't need another half-inch on that basis.

Consider what a tile manufacturer has to say... (I'm not going to cut and paste their extensive text here, or rewrite it all) but for one thing they specifically mention setting the backer board in a mortar bed, not "gluing" it down. I'd also venture to sneak in that if you really want "the best" (and will you pay for it these days) look at the "old fashoned mortar bed" (TCNA (Method F145-02)) mentioned at the end of their article. That, of course, means you need to establish an adequately rigid base 3/4" or 1-1/4" + tile thickness below the surrounding floor level, which is why it's not popular these days. But it was a VERY good method, as a lot of old houses demonstrate.

Kinsman Tile

Well technically it is plywood, it's just not very good plywood. Having said that I've seen flooring guys use a product that looked very much like luan that was no more than an 1/8 of an inch thick to get the level they needed. This was in a hospital remodel so it was definitely up to code and it went under a commercial grade thermo-sealed floor so it should be good for just about any application unless your subfloor is really atrocious. Ask around at a dedicated flooring supply store and they should be able to point you in the right direction.