H1B Mexico Visa

I read the following statement from https://www.nvars.com/use/wEntry.jsp

"ATTENTION
Due to an April 1, 2002 change in regulations, applicants will only be able to re-enter the United States if they are found eligible for a new visa and actually have the visa stamped in their passport. I-94 forms (even if valid), accompanied by previous expired visas, will no longer be valid for the automatic re-entry of persons from Canada or Mexico if during their visit they applied for a new visa that has not, in fact, been issued"


Is that true? I reviewed lots of posts here about getting Visa in Mexico and one can still return USA if you got checked. This means you can go back to USA with a valid I-94.

Anyone can clear this confusion with own experience. Thanks a lot.