I tested the relay by applying 5 v. to the control pin. The ProMini was not yet on the board, so I couldn't test it from the ProMini. Well, that burned out the relay.
So with further experimentation, I discovered that that UV diode in the relay is not protected by any internal current limiting. If I had read the data sheet very carefully, I may have deduced that, but is not stated in the data sheet.
This is true of most (all?) optoisolators.
Inside the chip it's just a LED. The same rules apply to LEDs inside optoisolators as any other LED.
They can't really add a resistor because they don't know what voltage you're going to use to drive it.