Exposed Grouped Filters on content type don't work

When I create an exposed filter with Grouped Filters, searching always returns results appropriate to the first option, even if I select the second option.

For example:

I want to offer a pair of radio buttons with fulltext search, letting the user search either all content (or rather, a set of about 12 content types) or just tools (a single content type).

I created a node index view with three filters:
* Indexed Content: Status = Published
* Search: Fulltext search (exposed)
* Indexed Content: Content type (exposed)

The Content type filter is set up as Grouped Filters, with a default option called Entire Site, which has "is one of" and then about a dozen content types selected, and another option called Tools Only, which has "is one of" and then just the Tools content type selected.

When I use this search, I get the same results whether I select Entire Site or Tools Only - which means I get non-tools in my search results, in both cases.

I have created a similar view using Core Search, and it DOES work - returning a different set for "Entire Site" vs. "Tools Only", so I think the problem is related to Search API.

Any suggestions?

Thank you!

Kristi