Thanks, guys, but for some reason Ira's post prompted me to go looking, and I found out that it's a bug in Mail 13.4.
When I quit and relaunch Mail, the remote content appears only after I hit the "Load remote content" button, at which point the button disappears.
Subsequently, though, when I click away from the particular email and then back to it, both the remote content and the "Load..." button are there.
(I was never worried about it being a malware problem, because I click on the button only when the sender is a known reliable entity.)
