No that is exactly what it means.
Again, salve comes from the verb salvere, which refers to health, wellness, and salvation. Towards a person, saying "Salve" is rather like saying "Are you well?"
My "Classic Latin-English and English-Latin Dictionary" notes the following:
"save, v. tr., ... 3. God save you, salve, ave, salvere te jubeo (at meeting), salve et vale (at parting)"
"salve, salveo, v. (salvus), to be well in health, found chiefly in the forms salve, salvete, salveto, salvebis, salvere (jubeo), used by the Romans as a greeting, Good day! I hope you are well? How are you? a. in welcoming a person, Good day! good morning! ... b. in taking farewell, good-bye! God be with you! vale, salve"
There is no entry for "salvare" because this is a later ecclesiastical derived word of salvere.
Again, "Gruss Gott" is also respectful greeting in Bavaria, but it means much more than "Hello", although it is used to say "Hello".
Just as "Vaya con Dios" in Spanish means more than "Goodbye".
Obviously, we aren't asking Blessed Mary "How are you doing?", nor are we saying "God save you" to her.
This leads us back to what exactly we are trying to communicate using the imperative form (a command) of a verb meaning "to be well, to be in good health, to save".
Again, I have no objection to translating it "Hail", because "Hail" is the Anglo-Saxon form of the German "Heil" which means "to be well, to be in good health, to be whole, to save", exactly the same meanings as "salvere".
These words are all related, as the German form follows the Greek in coming down from the Indo-European original in turning the "s" to an "h", thus in Greek "holos".
You keep trying to run away from what is right there in front of you, but you can't escape the meaning.
I thought that Goodbye was originally God be with ye.