Ok thanks for that.
It's interesting that Silvia Duran Tirado, the Cuban Embassy staffer that Oswald met at the Cuban consulate in Mexico City, said she asked him that if he was a member of the CPUSA (as he falsely told her) why didn't he have them and the Cuban government arrange the visa.
From her HSCA testimony:
TIRADO - ....What I said is that when he said he was a member of the Party, of the Communist Party, the American, I said why don't they arrange, the Party, your Party with the Cuban Party, and he said that he didn't have time to do it.
CORNWELL - Did you ask him why hw didn't just have the Communist Party arrange his trip to Cuba?
TIRADO - Yes.
CORNWELL - the Cuban Communist Party? He just said he didn't have time?
TIRADO - Yes. Because there was a manner to do it. I mean, we get, for instance, the visa directly from Cuba and saying give the visa to this people that's coming and somebody say oh, yes, you have you visa here.
So apparently if you were a member of the CPUSA the travel restrictions didn't apply? Or they could just get around them by having the Cuban government prepare the visa in advance? That's pretty odd.
Full testimony here:
http://mcadams.posc.mu.edu/russ/m_j_russ/hscadurn.htm