Why doesn't $h\rightarrow \gamma\gamma$ rule out two higgs doublet models? 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?
 A: First of all, I'd like to make some remarks:


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*The spectrum of a 2HDM (two-Higgs doublet model) is more complex than you think. There are 2 CP-even bosons ($h$, $H$), a charged scalar ($H^\pm$) and a CP-odd scalar ($A^0$). Usually, we identify the lightest CP-even boson as the scalar particle found at the LHC in 2012 and we assume that the other scalars are heavier than 126 GeV.

*When $h\to \gamma \gamma$ is computed in the Standard Model, there is also a contribution where $W^\pm$ bosons run in the loop.

*I think that the only channel with significant statistic is $\gamma\gamma$. In the strength signals listed in PDG, you'll see that $\tau\tau$, $bb$ and $ZZ$ were reported only at Tevatron. Maybe an experimental physicist could give us more details about these results! 

After this small introduction, I'll try to answer your question:
Assuming that a model with two doublets provides a suitable description of nature, then there are two modifications that should be done to the computation of $h\to\gamma\gamma$ in the Standard Model:


*

*The couplings of the SM higgs-like boson $h$ with the top and with $W^\pm$ bosons are modified by two new parameters: (i) the ratio of the two vev's $\tan \beta$ and (ii) the mixing angle of the two CP-even scalars $\alpha$ (cf table 2 of 1106.0034). For example $$g_{WWh}=g_{WWh}^{\text{SM}} \cos(\beta-\alpha)$$ and similar expressions can be found for the other couplings. In particular, we obtain SM-like couplings in the limit where $|\alpha-\beta|\to \pi/2$.

*There is also a new contribution with a charged Higgs boson running in the loop, but this one decouples from the low-energy theory if $H^\pm$ is heavy enough.
So, as far as these new scalars are supposed to be heavy and the Higgs couplings with the top and $W^\pm$ are similar to those of the SM ($|\alpha-\beta|\to \pi/2$), then we can always be consistent with the measurement of $h\to\gamma\gamma$ without excluding this model. This is sometimes called the decoupling limit and there are several works in the literature which study the impact of LHC measurements in the parameters of a 2HDM (cf 1305.2424, for example).
A: Your guess goes into the correct direction. There are other particles contributing to 
$h \to \gamma \gamma$, such as $W^\pm$ bosons. 
Moreover, these exact branching fractions depend on the parameters of the model. While a scenario with no coupling between the scalar at 125 GeV and the top looks very disfavored, the same model with different parameters might do just fine.
