In that scenario he wasn't just close to you but close to several others as well. I'd have no problem in stating without fear that Oswald was there as well. He wasn't there so the question is of course completely hypothetical..
Of course it is hypothetical but not because he was or was not there but because we were not there.
The fact he was arrested immediately might brought those several people to rethink what they saw that day. The frenzy and chaos were huge, Oswald was pushed and pulled all around DPD, news were galloping every minute, tensions about communism and Russia were high... If I would be a Prayer Person and saw Oswald on those steps I would sit down and think seriously if to say I saw him or not. In all that circumstances the only solution was to say not seeing him that day.
If you think about Wesley Frazier for example I bet he was under huge pressure and fear of being accused as Oswald accomplice so he maybe decided do make some things up.
After initial chock people simply had to stick to theirs stories and do not forget there were threats and unsolved deaths of witnesses which can only make us conclude that not everything was as we know today. And we do not know it all.
