Oswald probably wouldn't have admitted to it anyway. He'd have used the stand as a soapbox for ideology "The US government is conspiring against me because I am a member of the Communist party.". He'd probably have supported the conspiracy theories too, like Sirhan Sirhan does. But he would have been convicted.
Didn't Oswald defect to the USSR? In that case, he would be a foreigner who killed the American President (or considered a traitor by many instead). That's all the reason some Texans would need for revenge.
Case Closed.