You are the correct one. Mechanic can only pull back cards that are of the type "Play on a Base."
My argument was that the Rampage action does not state "Play on a base:" it is an action card that effects a base when played.
This is 100% correct. The wording "that can be played on a base" is not a license to pull back any card that that has an effect at or on a base (like Rampage, Terraforming or Broadside for example) but rather limits it to only actions that literally say they are played on a base.