He wasn't formally terminated. Instead, he was told that his next checkride would be with the director of training. The message was, "Find a new job in the interim" because this pilot and the head of training did not like each other and the pilot outright blamed the director of training for his "training difficulties". As for an entry in his PRIA records, sometimes the truth can be somewhat obscured. If, for example, someone is doing poorly in upgrade training and elects to discontinue or is discontinued by the company, it's not quite the same on the records as a formal checkride failure. At least that's how I understand it.
If you're interested in how often someone can or should be able to fail checkrides and still continue as a professional pilot, there was a thread on that topic a few weeks ago with a lot of opinions offered. Try a search if you'd like to read more.