Kidnappings, Banditos, etc
Generally you are not going to get kidnapped strolling around shopping for bargains in a border town. The trouble tends to happen on the road out in the sticks far from any town or police. I've done a lot of driving in Mexico, a couple of times to Guaymas, once to Mazatlan, and cris-crossing the country from San Miguel over to Vera Cruz and back to Acupulco and Ixtapa, circling back around to San Miguel. Never any problems. But I have heard horror stories from others and in most cases they were driving a shiny new car. My driving was behind the wheel of a 10-year old Galaxie or an old Datsun. We blended in just fine and in some cases the license plates had the same color scheme as ours which helped even more.
If you just want to go across for the day and do some bargain hunting or pick up some good Mexican booze for cheap, you shouldn't have any problem and as the immigration site advised, the passport thing is only for air travelers. If you walk across you shouldn't have any trouble as long as you have a driver's license with your photo on it. A birth certificate is always a good idea, but keep in mind, this is the stuff you need to get back into the states. You can walk into Mexico without any documents at all, but you'll need some kind of ID to get through U.S. customs when you return.
I can attest to this because I attended a wedding in Chula Vista, south of San Diego, and the reception was held in Tijuana. Nobody needed any special papers or a Tijuana reception would have been a logistical nightmare. We went across in vans to the reception hall. At the end of the evening we were among the last to leave. We allowed some ladies onto the last van and decided we'd walk back across and get a cab to the house in Chula Vista. We had no problem with only our driver's licenses on us. And, because the Tijuana border crossing is the busiest on the planet, we beat the people home who were in the vans still waiting in line to get across! Nogales is much less busy and hectic compared to Tijuana and should be a relatively painless crossing.