The Turkish r
It's unvoiced isn't it? That's what gives it a slight ş sound to it. Also, it often isn't as obviously rolled, but that's because it's unvoiced!
Am I completely wrong, because this would make a lot of sense to me.
This is totally ture. It is only partially unvoiced, which is why it almost sounds like a ş to the untrained ear. Also, Turkish R's in general are almost never rolled! They only do this when wanted to be really emphatic (some people in the East and South of the country do this normally however).