Of course not. Oswald was a wrong man on the wrong place. Because of his life in USSR and coming back to the US, he was a person of interest. If he did not left TSBD in panic, if he was calm and waited everything to settle that day, most probably he would not be charged. When he saw the "assassination" he left TSBD in panic knowing that he will be prime suspect. I am sure you would do the same.
How did he know the "assassination" occurred? How did he know he would be the suspect? If he was having lunch at the time of the shooting, then came out to see what happened, how did he know anything about what happened? People around the TSBD were unsure as to what happened. They heard shots but weren't' sure whether the president was hit or not.
According to the people who where there and from photos and films, it was chaos. Nobody really knew what happened. It was all confusion and rumors. But you think Oswald saw all of this, concluded the president was shot, and then further concluded I better run because I'm going to be blamed? Why not stay and show he couldn't have done it?