To get married (have someone perform a marriage ceremony for you and your partner) is always grammatically passive. The speaker could say I married last year with the same meaning, but we usually use got married in everyday conversation.
Sentences like The priest married her are always potentially ambiguous (out of context). In the old British TV sitcom All Gas and Gaiters there was an episode where the Bishop's chaplain meets a female friend and reports "She has asked me to marry her". In fact she had asked him to officiate at her wedding to another man, but the other characters understand that she has proposed to the chaplain - lots of comic misunderstandings ensue. (In real life he would have realised that what he had said was ambiguous and quickly made it clear!)