In two higgs doublet models we introduce a down-type Higgs as well as an up type Higgs and typically (as I understand it) we take the down-type to be the 126 GeV resonance and the up type to be somewhat heavier, around the TeV scale.
At this point we've measured the 126 GeV resonance and its decays to $\gamma\gamma, \tau\tau,bb, WW , ... $. In order to predict the rate of $\gamma\gamma$ production correctly we need the top quarks to run in the loop, and hence a coupling between the top and the Higgs. Therefore, it seems the observation of this channel already eliminates the possibility that the observed Higgs is only of the down type since it couples to the up type quarks (I'm envisioning a SUSY scenario where only the down-type higgs only couples to the down-type quarks).
However, I've never heard anyone mention that this observation firmly rules out SUSY models, for example. Is it because $h\rightarrow \gamma\gamma$ can in principle be produced by some other particles in the loop with just the right masses to predict the rate given by the SM loop with tops or is there a better reason?