They are funded by the government and hence to some extent controlled by it - for instance, the Erdogan government decided to have TRT make a new channel broadcasting in Kurdish - but it's not as if they ask the government's permission or approval for every show they make. Certainly, the government would have been able to prevent this show from being made and broadcast, but that would've been considered censorship, because the government isn't supposed to actively decide about which programs to broadcast and which not. So saying "the government aired it" is nonsense; the only accusation that makes sense is the government failed to prevent it from being aired, apparently preferring to offend an ally rather than being seen censoring things in defense of said ally. Admittedly, most Western governments in comparable situations tend to go the other route - like the way the Obama government opened itself to accusations of hypocrisy and ignoring human rights when it tried to avoid insulting Turkey in the Armenian Genocide incident last month. Israel's reaction was rather different, if you recall that incident with the Turkish ambassador, a few months ago now.