since is used about something that happened regularly or continuously over a period of time, either until now or until some event in the past.
Note that getting married refers to a one-time event - the wedding day-, whereas being married refers to a state which normally occurs continuously for a long period of time. When you use since with a one-time event, it means that it occurred during the interval between the specified time and now. Consider these two sentences:
They have been married since 2005 - they married in 2005 and still are married
They got married since 2005 - they married sometime between 2005 and now, and it is not specified whether they are still married.
It certainly is unconventional to use since to describe a one-time event, but it is not that unusual and it doesn't cause confusion. The fact that they later got divorced does not affect the fact that the marriage event took place.
The use of present perfect have gotten married is uncommon, but does occur, as this NGram shows.