That's not what we're saying.

We have observed a particle whose properties match what we would expect to see from the Higgs Boson at our current levels of data and sensitivity. This is not based on the value of the mass. We saw three decay modes with consistent excesses at a specific mass, and those decay modes match expected Higgs decays (H → γ γ, H → W W, H → Z Z). There are other decays that don't show an excess (H → τ τ, H → b b), but we don't expect nearly as much sensitivity in those channels yet. We excluded the other mass ranges in the same way: the sensitive decay modes in those regions did not show any excess.

There are many properties still to be analyzed, such as spin and branching ratios. There's a good post at Quantum Diaries about possible values for the spin. I actually hope the branching ratios are different from Standard Model expectations, since that would indicate a massive new particle which could be a dark matter candidate or lead to other new physics.