Both of the LHC fluctuations are at what's known as the two-sigma level - in other words, it's two standard deviations away from just being random chance - while the Fermilab result is one-sigma. Two-sigma means there's better than a 95% chance that there really is something at those energy levels, but even 95% isn't terribly convincing to the physics community. A discovery needs to reach five-sigma levels of certainty, or 99.99994% certain, before it can be considered a discovery. I went from physics to biology, and it makes me sad what passes for convincing in the biological science community. Personally, I am betting that there is no Higgs. My guess is we are going to find something else here that further confounds our current model of matter. A physics prof of mine once said something to the extent of: "Consider that mass and gravitational potential are always proportional. Why? We have no reason for this." My gut tells me that mass and gravity are one in the same. Not that particles acquire mass by interacting with a field, but that mass is a relative characteristic, -the quality of interaction of particles.
TL;DR: not only is the "Standard" model flawed, but it is substantially so the further we research it.