I agree iTunes is counterintuitive and confusing. Poorly designed - it seems to be getting less user-friendly with each iteration. It feels more like a Windows program each time there is a significant new version.
With respect to this particular problem, I had (or thought I had) the same issue. I wanted to put songs on the iPhone but couldn't, even after turning off iTunes match on the computer. For me, the problem turned out to be that iTunes match was off in iTunes on the computer, but was still switched on on my iPhone. On the iPhone, I went to Settings>iTunes and App Store>iTunes Match and switched it off.