My "friend" (B2 Multiple-Entry Tourist Visa holder) recently entered from Mexico to the USA twice, about 10 days apart.
The first entry was via the CrossBorder Express (CBX), over from an inbound flight at TIJ.
The second entry was via the Otay Mesa Port of Entry, personal vehicle lanes.
I was with my friend during the 2nd entry. My friend was asked "Onde você vai ficar?" and answered "San Diego." Then the officer asked, "Are you going to stay in San Diego during the entire duration of your trip?" to which my friend answered "No, I also want to visit Los Angeles."
The officer then advised that my friend should go into the building next to the vehicle lanes and pay $6 to get an I-94 "Permit" and get an entry stamp on the passport. It was at this point my friend realized the passport was missing an entry stamp from the arrival via CBX. The officer explained that someone who intends to stay only in San Diego ("up to Del Mar" in his words) would not need to do this and that the same rule applies at CBX, so it would be normal for my friend to be missing both the I-94 and the entry stamp.
The I-94 was issued, passport stamped, and my friend entered the US without problems.
However, I am posting this question because in my nearly 30 years experience as a "user" of the U.S. Immigration System, I have never heard of this rule. A Google Search for "I-94 land border" yields tons of postings about a different rule - the one that says you can enter via land border on an expired visa using a valid I-94. Not applicable here.
As a side note, all the Otay Mesa border staff we interacted with refer to the I-94 as a "Permit" or "Permiso", even though I believe this is not technically the correct term. Very confusing.
TL, DR
What exactly is the rule that says a tourist visa holder entering via land border and staying near the port of entry does not need an I-94 and passport entry stamp? What is the exact distance the person is allowed to travel from the Port Of Entry? What is the legal status of someone who's entered with no stamp and no I-94 under such rules?