He had the rest of his life to be worried about. That was borne out in the problems he had with the busybodies giving him static about driving the killer to work.
How many times do you hear people say they are innocent and have nothing to fear? Ask the innocent people who Henry Wade got in his clutches how that went, first time around.
Best to hedge one's bets given that atmosphere.
Once again you are not making any sense. An innocent and uninvolved Frazier had no incentive to lie. And most certainly he did not have an incentive to lie and tell the DPD something they didn't want to hear!
The DPD found a bag that was big enough to have contained a broken down rifle. Early on, with Oswald having been arrested, they were convinced they had their man. They also knew that Frazier drove Oswald to work that morning. So, the DPD wanted to hear from Frazier that they had the correct bag and that it was indeed big enough to contain a rifle, right? Telling them exactly that would have gotten Frazier out of trouble, but that would have been a lie!
But he did not tell them that. Instead he claimed, like an innocent person would do, that they had the wrong bag and that Oswald's bag was much smaller. Now, if that was a lie, it was a pretty stupid one, because the DPD could conclude that he was lying to protect Oswald and maybe himself as a complicit.
How many times do you hear people say they are innocent and have nothing to fear? Ask the innocent people who Henry Wade got in his clutches how that went, first time around. Could that possibly include Oswald as well?