It seems to be the accepted use these days. I disagree with that use but I don't have a better term and don't want to add to the confusion. But you're absolutely right that an exposed service and an API are different in many fundamental respects. I think the confusion is rooted in the gray area called remote procedure calls, if you implement your service exposure as a remote procedure call (and many of the early ones were done in just that fashion) then the difference is almost moot.

Maybe WSI would be a better moniker? (Web Service Interface)?