With or without New Visa Stamp

Urgent! Landed over the weekend via driving and going to be interviwed at the US Consulate in Toronto for new H1-B visa stamp. I was told that, with the new visa stamp, I will have a record on my passport for reentering to the U.S. But if I choose not go to get the new visa stamp, then there won't be any record of reentry to U.S. on my passport. Is this correct? I thought at the port of entry, you will have your passport stamped anyway no matter what.

Thanks.