I think it depends on the border crossing. At San Ysidro you can walk across and probably not get checked. I've walked across into mexico there a number of times (visa runs for TN) and never been checked, not even my passport. Granted I didn't have a bag with me. They tend to have a couple of guards who seem to check people occasionally, but I suspect if you were to walk across with a backpack behind a group of old ladies with luggage you'd probably be ok.