Some news sites read the Switch's open source credits crediting the FreeBSD project and ran with the headline "Switch OS based on FreeBSD". By the same measure, people should call Windows "based on FreeBSD" because the kernel uses BSD code or used to at least. It's sub par reporting that turned into an urban legend.
The PS3, PS4 and PS5 operating systems are systems based on the FreeBSD kernel, which is probably why it's tempting to think the Switch would be too.