I spent some time pondering the problem, then suddenly remembered that there was some coding required in the srcsafe.ini file to tell VSS put the history in commented lines.
I located the srcsafe.ini file of a project that was behaving as desired, and compared it with the one for my new project. I found the following lines in the correctly-behaving .ini file:
Keyword_Masks = *.cs, *.sql
Shadow =
[Keyword Comments]
*.cs = "//"
*.sql = "--"
The Keyword_Masks and Shadow keywords are placed in the .ini file after the UseHelperService. I suppose the Keyword_Masks (with comma-separated values) tell VSS which file types to place the history (I don't know what Shadow signifies, but since it occurs in all of our projects I didn't want to omit it and find out it caused something subtly wrong later).
The new [Keyword Comments] section occurs immediately afterwards (and before the [Timezone] section. This obviously tells VSS which characters to use for line comments, and for which file type.
And that did it!
Note that if you're using Visual Basic, this will be coded as *.vb. Obviously. And you don't have to include Sql; in this case our VSS project happened to contain solution and project files with stored procedures that we were also keeping in VSS.