So this is embarrassing. But there's a moral at the end of the story.
I was obsessing about this problem. It didn't feel like a bug. It felt like a setting. I recalled that I used to prefer Safari to always download pdfs.
Then it began to dawn on me that there might be a Terminal command that affects Safari's ability to display pdfs inline.
Some minutes of googling produced this Terminal command, which forces Safari to always download pdfs:
defaults write com.apple.Safari WebKitOmitPDFSupport -bool YES [Disables native pdf viewing in Safari.]
Some of the sites noting this were pretty old, but others were newer. So, I guessed that I'd applied this Terminal command in the past. With Safari off, I entered the following in Terminal
defaults write com.apple.Safari WebKitOmitPDFSupport -bool NO [Enables native pdf viewing in Safari.]
Worked like a charm in Safari 5.1.7, Lion 10.7.4.
BTW, Safari's native pdf support has improved so much that it's a better way to deal with pdfs, unless you always want to save the pdf.
Oh, and that moral I promised? Pay attention when you use "secret" settings using Terminal. Some, at least, persist even when the software is updated. It might even be worthwhile to keep notes.