I think Bitcoin being banned means all other alt coins will be banned as well since they are all in the same community, it is just that Bitcoin is the most dominant among those. Also, unlike individual people, the rulers are group of people to decide where in they will decide on the aggregate part of the crytp community and not only on a single part of it.
Diffenitely what you said was right. I guess when you say bitcoin literally bitcoin alone but other altcoins consider bitcoin as the main source for their trading because most of the population only access bitcoin first before buying and trading to other cryptocurrency. So when the government ban bitcoin it would probably include all altcoins.