The termination will be meaningless unless the applicant is choses to discuss it in depth. Most, if not all, HR departments currently only allow the dates of employment to be released to prospective employers due to the possibility of liability. I personally know of pilots terminated from 121 carriers for much more serious events (safety, walking off a flight full of passengers because they had been given incorrect performance data which they could not determine was for a different subtype, leaving the jet and taking the logbook with them because they were angry with Mx, a student in class harrassing a gay flight attendent during wet ditch training etc.) Also, before you say it, yes this is recent, within the last 5 years. As far as the old boy network, it doesn't work very well for the same libality concerns and, often, the reverse. The sooner a problem employee is hired with another carrier, the clock stops on potential damages.
Having seen it from the other side of the desk, give your dates of employment, don't lie but don't throw yourself under the bus, and learn from your mistakes.
By the way, many of these "problem" pilots rehabed their carriers and have not had furthur problems, so most of the time the system works. Also, just because someone doesn't fit in one airline doesn't mean they won't be just what another one is looking for. It really is a wonderful industry with a place for just about all of us.