It depends on what countries you’re going to. Not all are signatories to the carnet agreement. If memory serves, most Latin American countries don’t use carnets. On a shoot in Argentina years ago we had a letter from their tourism board, on letterhead, inviting us to shoot there. We talked our way through customs with that, although technically we should have been using a local company for short term import-export of the gear.
I’ve been doing European shoots for a company about once a year since 1999. The Producer there has tremendous experience in international travel. Last year was the first year they didn’t purchase a carnet. The producer reasoned they were expensive, a hassle, and MOST of the time the customs folks didn’t seem too thrilled to have to deal with them. He thinks that most of Europe is OK without a carnet.
And that’s the point – customs has a great deal of latitude in how they deal with you. Are they having a good day? Bad day? Maybe they’re busy and don’t want to deal with the carnet paperwork? Maybe they’ve just been given directions to crack down on TV crews? If I was producing, I’d have a carnet any time I was traveling to shoot in a signatory country. I just have a low tolerance for uncertainty.
As for getting back in to the US (if you don’t have a carnet), back in the day when I used to commonly have shoots in Canada I used a Certificate of Registration. This was a (free!) US customs form I filled out with all the gear info, then I had it stamped by US customs on my way out of the country. If there was any questions about the gear when returning I had paperwork showing that I hadn’t bought it overseas. On a quick google search I found this – https://forms.cbp.gov/pdf/CBP_Form_4455.pdf – which looks different than the old form but seems to do the same thing. I would suggest having a friendly chat with US customs to make sure this is the right form to use.