If the bridge sites pass the test of being legitimately useful information rather than just spammy then I wouldn't consider what they are doing as black hat. This test is subjective or at the mercy of Google's current algorithm.

If they are keyword stuffed junk then your SEO people are right penguin slammed keyword stuffing hard. I know because I was using these tactics back then. On the other hand a keyword specific micro site with useful information can rank and likely eventually pass on useful pagerank to the main site.

The question I don't have the answer to is the period of time the site becomes beneficial. If you buy a new domain and setup a micro site I personally think it will take a year or more before the linked domain can benefit based on what I've seen. I base this on the fact when the micro site starts to rank itself and receives traffic. At that point I think it is safe to assume some rank is being passed onto the main site.

So if I were in your shoes I'd analyze the age of the bridge/micro site, quality of content and the ranking for the targeted keywords for that domain to decide if your competition is benefitting from it.