Getting ready to install porcelain floor tiles. We're going to use
those
little plastic spacers to establish grout lines. It clearly says on
the
package to remove the spacers prior to grouting. There is a tool
especially
made for removing these things.

Installer (or perhaps soon to be ex-installer) says he plans on just
leaving
them in and grouting on top of them. This seems crazy to me. Is this
commonly done?

If you are using the spacers correctly, they should stick up from the floor.
There's no way that you could leave them in place.

These are the little "+" pieces. You stand them up between the tiles. The
cross part of the "+" (the "-" part) fits on top of the tile. The bottom
part of the "+" gives you the gap. The top part of the "+" gives you
something to grab to remove them.