Of course 4.Bxc6 dxc6 is the better move for Black: 4...bxc6 5.0-0 will be threatening to take on e5, and something like 5...d6 will limit the range of the f8 bishop.
Since white cannot get in something like 5.d2-d4 easily, Black will always get an improved exchange proper (where he did not have to spare a move on ...a6).
A better way to play like that for white is 1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.d3 Bc5 5.Bxc6, as the bishop is not well placed at c5.
I will not argue about your first statement. I think any example will have limited pedagogic value regardless of the reason.
I distinctly remember saying "I consider dxc6 better," and gave my reasons for doing so, pointing out that Nxe5 was not best. I did not want to give 3..a6 or 3..Nf6 because I thought showing why Bxc6 does not work yet is enough to help the reader figure out what he is going to do next. I could be wrong. In any case I never claimed to have the absolute truth, and certainly my understanding of these things is arguable at best. But my intention is to help and if I did that then the other consequences may be bearable.