$K\to \pi \gamma$ decay I was asked the following question in an exercise sheet:

The decay $K \to \pi\gamma$ is absolutely forbidden by a certain
  conservation law, which is believed to hold exactly. Which
  conservation law is this?

The answer states that the electromagnetic interaction conserves strangness number and that therefore the above decay is not possible.
My question is, how can they be so sure that we have an electromagnetic interaction here? Couldn't I fore example have the following situation

If I'm not mistaken the lhs would correspond to a $K^{+}$ and the rhs to a $\pi^+$ and since they interact via the weak interaction strangness number is not conserved...
EDIT: As noted by @annav in the comments the original question didn't make sense in this form, since the charge on the lhs was $0$ but on the rhs $1$. This problem can be corrected by considering $K^+$ instead of $\bar K^0$.
 A: Go to the PDG listing, detailing the decays of the charged K, and the exclusion limits of disallowed ones.
You see that $K^+\to \pi^+ \gamma$ is excluded by angular momentum, an exact conservation law. In the rest frame of the K, the decay product particles fly off back-to-back. The photon's spin has to be $\pm 1$, along its direction, but both K and $\pi$ are spinless, so nothing can offset its spin along that axis. So it is impossible to conserve angular momentum in this decay.
Strangeness, by contrast,  is only an approximately conserved number, and violated by the weak interactions, as your tree diagram indicates. In fact, the decay $K^+\to \pi^+ \gamma \gamma$ also violates it, but is now allowed, and does occur, as you confirm from the listings.
The "answer" you cite 

The answer states that the electromagnetic interaction conserves strangness number and that therefore the above decay is not possible.

is then unsound and abusive: these decays are both weak and EM, and strangeness (along with other, more recondite, approximate rules such as $\Delta S= \Delta Q$) is violated just fine at this level, by the weak interactions, in the SM.  It is angular momentum that puts a stop to it.
