I think your friend was right.
The card states "You own more cities with Temples than any other player".
It doesn't matter who "owns" the temple just who owns the city.
So in this case you'd count cities that you own (3) that also have Temples in them.
The 4th temple was not in your city so doesn't meet the criteria of you owning a city that has a temple in it.
Leigh is quite right. The owning part of the objective is important. It may seem unfair to you in this case, but this wording also ensure that temples in your cities under foreign cultural influence still count toward the objective. So it is worded like that to maintain balance.