Alright, I've got it. I *am* a bit concerned over the ambiguous wording of this rule in the Learn to Play guide. The only place this is mentioned is in the Action rules on page 10 and it says "A ship that overlaps another ship cannot perform its action"...by the time you are in the action phase a ship can't overlap another ship, which is potentially confusing to new players. It might be worth putting this information in the Movement rules section and/or changing the wording to disambiguate.
So the rule for overlapping at the end of movement is to move a ship back until the bases are not overlapping any more. The ships are then "touching". The rules then say that actions can't be performed by a ship that is overlapping another ship. This seems strange since by the time you are going to execute actions, your ships will never be overlapping. I'm trying to determine whether this was a misuse of the word overlapping in the rule book (should have said "touching"?), or if I'm rather misunderstanding something.