I don't know if it works for the example of the slow pushups, but couldn't slow exercises be counterproductive when the desired result is speed- or power-related, assuming some sort of precedent in the proficiency of the athlete in power or speed? For example, I had an 8'4" broad jump at last measure, and that solely because I essentially do plyometrics when I train parkour. If I were to start cycling (long slow distance, not sprinting) a lot, would my broad jump decrease, if slightly?
With the right combination of details, it would actually be possible, but you have to consider how difficult it is to argue for a statement like exercise being counterproductive (producing a direct negative effect above and beyond doing nothing at all), as opposed to the much easier claim of being less effective or worthless or a waste of time (where it just doesn't do anything useful but is not necessarily worse than doing nothing at all).
So, in your example, it takes a much harder combination of factors to do worse with cycling than with no exercise, and that's much harder to do (for example you might have to be in a situation where you are eating very little food and actually getting part of the muscles to be catabolized during exercise for energy, or atrophied etc, or having near maxed out your potential toward speed adaptations so that trying to increase endurance forces you to replace some of those adaptations, which is also very hard to do and only works if you prevent muscle growth and other all-around good adaptations).
In addition, again it's not about slow and long distances vs sprinting, even with slow and long distances, if you are going up very steep inclines with a very high-ratio gear, so that every slow pedaling is a bit like doing a one-leg squat, that would again not be endurance at all but be mostly a strength exercise, one which fully engages your fast-twitch fibers too and might not be sustainable for very long, and could very well help your broad jump.
