Welcome to the forum, Guitarboo88.
You are right - and your cousin is wrong:
@rulebook:
Air Units
Each air unit that moves in the Combat Move phase must generally reserve
part of its Move value for the Noncombat Move phase, when it must return
to a safe landing place using its remaining movement. See page 23 for
examples.
An air unit’s movement in any complete turn is limited to its total Move
value. For example, a bomber has Move 6, but it cannot move 6 spaces to
end its movement in a hostile space. It must save enough movement points
to get to a friendly territory where it can land. A fighter can move up to its
full Move value of 4 to attack in a sea zone, but only if a carrier could be
there for it to land on by the end of the Mobilize New Units phase.
HTH :-)