Can I do a border run with a new passport if I have already done two border runs?

Two months ago I did a visa run to Ban Pakkard. They said have to fly out the next time. Then I did my 30day extension.

I only had a couple more pages in my passport, so I got a new passport, empty except for the one stamp, of my visa expiring Sept 17th.

So I figured I could still do border run, as it's a completely new passport.

I was making reservation with the same visa run service, but they said , the last numbers would be on that new stamp, so they would know I've already done 2 border runs.

Is that true?