Belgium: proving that there is a worse way to do low-emission zones than the French and German method. At least the Belgian ones are free for compliant vehicles.

Assuming you're not rolling with the Swedish equivalent of rent-a-wreck, you're definitely allowed into Brussels and Antwerp's LEZ without a pass--anything Euro4 and newer (which was ten years ago) is good to go.

For Brussels, you're supposed to upload a copy of the vehicle registration here: https://lez.brussels/en/content/registration

For Antwerp, you can upload the registration here: https://www.slimnaarantwerpen.be/en/...r-your-vehicle

You can also allegedly use the day-pass vending machines in Antwerp to register your vehicle for free.

If you don't have a copy of the vehicle registration, you should hope you don't have any run-ins with the cops because it's illegal to drive without it--particularly outside Sweden where the cops won't have immediate access to the Swedish database. If they actually didn't include it, my vote is to get fined and tell Hertz it's their fine because it's their fault you couldn't register.

Also, the vehicle registration probably looks like this (image nicked from a Dutch Volvo enthusiast site's page about Volvo-shopping in Sweden):