Corbyn's commentary isn't on whether the claim is correct or not, his comments are on the fact that someone appearing as a military spokesman shouldn't be seen to be endorsing a particular political party or candidate, or advocating against them.
Personally, I don't think any of the current political party leaders - with the possible exception of that Farage dingbat - are stupid enough to actually resort to firing nuclear weapons, regardless of the situation. I don't expect that many foreign sources looking in see it as any different, likewise with the current American administration, although a Republican president is a scary concept.
Given that, I don't see that Corbyn being open about it is any different to everyone understanding that Cameron wouldn't be that idiotic either - Britain's nuclear arsenal is still just advanced sabre-rattling.
O.