I think you got it right.
It entirely depends on whether or not one (or both) of those getting married is Catholic or not. The Catholic Church does not teach (and has never taught) that only Catholics can validly marry. Marriage was a natural institution long before the Church ever existed. Non-Catholics still validly marry each other.
If one or both of those getting married is Catholic, though, then they are bound to follow the Church’s law on the subject, which states that Catholics are bound by the form of getting married in a Catholic Church. Catholics can (in certain circumstances) receive a dispensation from form and get married elsewhere. They would need to talk to their pastor about it, though. These are generally given when one party is Catholic and the other is not. They are not given just because the couple wants to have a destination wedding.