No. It was like that (where vi is just a lightweight recompile of vim) several years ago. Since then Arch has switched to using ex-vi[1], the closest thing to 'authentic' vi you can get nowadays.
Sounds reasonable. I was about to guess a similar thing. A minimal Debian install (perhaps Ubuntu and other child-distros as well?) installs a vim-tiny[1], which often throws people off[2].
The last time I used AIX (I believe it was 5.3), it had old-school vi on it. I would bet this is true of newer revisions of AIX, as well as other commercial UNIX(tm) systems. I would also not be surprised to learn that some/most of the BSD systems still use it.
I don't think any of the free BSDs distribute the classic vi by default anymore, but they've standardized on nvi rather than vim as their "enhanced vi" of choice.