I don't think this is the typical experience of humans. I grant that there's a lot of diversity, but I think the majority experience is that you get an intuitive approximation that you can override or refine by doing the self-in-other's-shoes thing.

I also don't think one should necessarily assume that one can introspect that how-it-seems-I-am-doing-it is equivalent to how-I-am-doing-it. Too many exceptions have been documented for that to seem wise.