I was going to explain that in my post above but this stuff is so hard to wrap your head around, espesially if you don't study Russian grammar in depth, that I just couldn't think up a good enough explanation at the time. Anyway, I think I might have come up with something cohesive now. You see, this whole thing with these "connectors" is just grammar. Say:

То, как он говорил, разозлило меня.

I intentionally put a subordinate clause right into the middle of the independent clause as I think it can show things more clearly. Let's think about "то" and its role in the independent clause.

То разозлило меня

1. То is the subject of this clause.
2. То is also a demonstrative pronoun, so it's semantic meaning is not clearly defined, instead it "absorbs" the meaning of the thing or idea it points at.
3. Now what is "как он говорил"? It's exactly what "то" points at.
4. Can "как он говорил" be a subject? No, it can't! So this is where this "то" comes in. Its purpose is to assume the role of the missing subject and glue the two sentences properly. Without it these two clauses are nothing but two different sentences. I personally like to call this a "blank" subject, object or sometimes a pointer (like туда).

This is why то, как works, as the pronoun то can be easily defined by как...

I hope this makes sense.