Do I need to transfer my tourist visa to my new passport after renewing it at the US Embassy?

I recently renewed my passport at the US Embassy. I received my new passport in the mail with a letter requesting Thai immigration to transfer my single entry tourist visa to my passport.

I just read a post from someone who went to Thai immigration for this purpose and the Thai immigration officer said it wasn't necessary to transfer the stamp (unlike me, he had an exemption stamp not a visa) to the new passport and that he should simply present both his old and new passports at the border and there would be no problem.

Are they likely to say the same to me? Or maybe this is one of those issues that's up to the discretion if the imm officer?