And yes, they are very similar. The rhythm of the vocal-melody in the verse is pretty much the same even if the end of the phrase in the stones-song contains more notes. And the structure of the melody with two repetitions of the main melodic phrase followed by a contrasting motive that's also rhytmically similar and of the same length in both cases makes it even more similar. Seems like he used the Stones-song as a blueprint/skeleton and filled it with his own notes. Nice catch...

EDIT:Semi-Cover though? Not sure what the definition is of that. The melody generally carry stronger weight than rhythm/structure so maybe it's like a quarter-cover or something...