Copyright covers all contributors and for opera, of course, this includes the librettists. I don't have the details off the top of my head right now, but in Puccini's case, I think he was working with a young librettist when he was an old man, so the librettist is the one who is still under copyright. And since he used different librettists for different operas, this is why some are still covered but not others.
The issue of rental is a different one. Once a work is in the public domain, if a company has the only set of parts available, they are under no obligation to make the work available for sale. There are several examples of public domain works that can only be rented, not purchased . . . .