I agree with ^^^ them. If you are asked, "Have you ever failed a checkride?" I would say flat out "nope." Now, if they specifically ask, "Have you ever failed any checkrides OR stage/phase checks?" I would say that I have not failed any End of Course Checkrides however yes, I did fail the Lesson ___ intermediate stage check in the ____ course." Then, most likely, the interviewer will ask you about what happened and what did you take away from the experience.

I went through a 141 with Examining Authority School and even if I knew the FAA didn't know about my EOC failure, I would still cough it up on an interview. It is not necessarily a bad thing to have failed a checkride as long as you learned something from it and can appreciate the value of the lesson you learned from it (this is what I believe an interviewer is looking for).

Just my $0.02