L'Hospitalet de Llobregat
I found the answer in the FAQ, sorry for re-ask here.
Q. Do card effects supercede the rules? (example: Hostile Press Corps)
A. In general, yes, but most of these effects are applied as modifications to existing rules. Hostile Press Corps, for example, takes an existing effect (the support check requirement for carried states) and applies it in a new context (every state, not just those genuinely carried by Kennedy). Any other rules which apply to this effect, such as the fact that the support check requirement is negated by media support, would continue to apply in this new context, however.
Then, Nixon doesn't do support checks.