You're right that there is no way of knowing what terms your competitors are targeting (nor will Google ever give us a tool for finding that out, as it's not in their interests to do so).
But I disagree with your suggestion - that googling for any of the likely terms will give you some useful information. AdWords is very closely targeted at the searcher's profile. If you search for a certain term, and that term does not generate your competitor's ads, that does not tell you whether the competitor is targeting that term. It only tells you that other advertisers are more closely targeting you. Also, you would have to repeat the search many times to get a meaningful sample. But doing that would itself distort your profile, and thus make the result even less reliable.
The only possible way of knowing what your competitors are targeting is to make an intelligent guess. Alternatively, don't bother, and focus instead on the terms that you should be targeting.