Teamwork feat question re: Mounted Combat

[Serisan]

If you and your mount/animal companion both have Escape Route and you are mounted, is it impossible to provoke attacks of opportunity for movement?

Ultimate Combat wrote:

Escape Route (Teamwork)

You have trained to watch your allies' backs, covering them as they make tactical withdraws.

Benefit: An ally who also has this feat provokes no attacks of opportunity for moving through squares adjacent to you or within your space.

[Bob Bob Bob]

Sure looks like it, yes. You're always sharing a space so any movement one of you makes better be within or adjacent to the other one (otherwise someone's teleported).