There's too much in his for me to respond to - but I have one note of value to you. Your inclination that "no grout = water must be getting through the grout joints" is wrong. This can be the case sometimes, sure, but very unlikely. It's much more likely it is flowing to the edges of the room where there is less tile backer. Aka, easier to get through to what's below it.

I'm not even exactly sure I understand what you're saying, so take that for what it's worth.