I agree "displays photos in ProPhotoRGB color space" is a bit vague. Here's what I believe to happen (ignoring soft proofing):
In Develop Module, the image is converted from raw (or whatever is the format of the image) to ProPhoto RGB. This conversion always takes place when an image is worked on in Develop Module. ProPhoto is Lightroom's working space, and it can't be changed. Assuming the monitor has a correct profile, the image is mapped from ProPhoto RGB to monitor colour space for display.
In Library Module, Lightroom displays the preview image. If there isn't a preview, it creates one. Previews are stored in Adobe RGB colour space (in jpeg files). When the image is displayed, obviously Lightroom maps the image to the monitor colour space, but this time from Adobe RGB.
I stand to be corrected by an Adobe insider, but this is what appears to happen.
Edit: I overlapped with Andrew, but I think we're saying compatible things.