No, when followed by a preposition, vicino is an adverb and does not vary. Vicino a means near to, close to, next to; vicino da means from a short distance; from close up.
Duo's version is modifying the verb. It seems weird to me when that verb is essere, because "is [in a position]" should really use stare, and sta vicino sounds right to me. Maybe it's an idiom or an archaic form? English did the same: "next the entrance" used to be normal.