Salvere = to greet,hail, to be in good health, etc.
Both words obviously have the same root origin, since the meaning of salvation is to be of good health or well in the soul.
http://www2.carthage.edu/outis/vocab3.html
Notes that "salutations, salvation" are derivatives of this verb.
Preventing "salvere" from retaining root meanings and thus forcing "salve" to have nothign to do with salvation is rather like taking the Bavarian greeting "Gruss Gott!" and claiming it means nothing more than "Hello!"
Would you really have us believe that "Salve Regina" meaning nothing more than "How are you doin' O Queen?"
Again, the question is not WHETHER it is a greeting, but rather, WHAT MANNER of greeting it is.
The English word "Hail" best translates "Salve". It's a respectful greeting (not a "hi, how are you doing?").