I respectfully disagree. Do a search, this has been discussed a bunch before, although I'll throw in my two cents on this thread too.
If you got a down (pink sheet, unsat) for a stage check in primary, you considered it a busted checkride at the time right? Many people have gotten them. The fact you got it isn't important, it is what you learned from it. (insert lesson about studying more, situational awareness, whatever you actually did learn from the incident here). Going all lawyer on the question (either on an application or during an in person interview) isn't the way to go in my opinion. "it wasn't an FAA ckride" "my ip was only a FAIP" "he wasn't a designated ck airman" etc. That makes you sound like you are debating the definition of is.
From what I've been able to gather, most interview processes are about figuring out what kind of person you are, your integrity, ability to play nice with others, etc. Not as much about your technical competence, that is what your ratings are for, or the sim ck for airlines that do sim cks. I'd rather go into an interview prepared to discuss one 'bust' on a initial training inter-stage ckride than worrying about if your integrity will ever be called into question.
For instance, the logbook examiner is looking through your logbook (or air force print outs, why is the U.S. Air Force the only place that doesn't use logbooks?) and they notice that you did your Fam13x twice, or whatever flight it was. And they ask, what happened here? How does that gybe with your application that says no ckride busts? Then you find yourself 'with some splaining to do.' not a good thing.
Short version. It was a checkride, if you did it twice, you busted it, put it down. I doubt it will affect your application but it might negatively affect your interview. Just my opinion and I'm already outnumbered 4 to 1 on this thread.
I see it as another version of the "I got a ticket when I was 16 in another state and it isn't on my record, do I put that down?" Well, if the application asks last 5 years, obviously no, if it asks have you ever had a ticket. I would say yes, whereas some might say no. Ask yourself what will make you most comfortable when you are in the interview room.