c being constant is now called into question.....c a constant and/or a speed limit is probably a localized or special phenomena by implication.
It doesn't call C being a constant into question. It only suggests that some things that aren't light might exceed that constant. We don't actually know what the implications might be because nobody has worked out a theory yet that would explain these observations (and they probably won't because this won't hold up), but there's nothing about them that require doubting the constancy of the speed of light and there have been a great many other experiments that have already confirmed it.