Could the screening thing maybe seem like too much, too soon? Like maybe too big of a gesture? Maybe he could make up some excuse for why the screening had to be cancelled, then ask her out to lunch or something instead (casual it up a bit). If she refuses or makes some excuse, then he knows for sure he's out.
If I'm not mistaken, Hammerhead mentioned that she'd try to invite someone to a previous date as well. In these sorts of situations, when you're 99% sure she's not interested, I find its better to just cut your losses. Either that or go down in flames, if that's your style.
I don't know that there's any rule for or against it but, unless there's some situation where you've been friends for a while, I find it really hard to imagine a woman not knowing that she's being asked out on a date. I'm sure those stories exist, but if you're doing it right there shouldn't be any ambiguity even without straight-up saying it.