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.
I drove over the border, perhaps Brownsville? I forget the name, but one of the last eastern border crossings.
Drove over in a camper van with European plates, didn't even realise had left the US until got to the Mexican side and went and sorted papers for the vehicle. No search, no check, just passports
