You are correct.
You need to be careful, because they are enticing with free and then trying to charge. Free subdomains are easier to obtain, but there are some domains in "off-TLDs" that can be obtained. The list of those changes over time.
Honestly, though, I wouldn't use those for an actual business. The conversation was about how to subvert using domains as identification.
Domain registration happens through an established registrar who collects fees. There are no free-as-in-beer top level domains that I’m aware of.
I would love to be wrong, because I own more than a couple domains myself.