My kids are still young enough that they are never anywhere without an immediate family member there too. The obvious exception is school/daycare, but I know that the state licensing checks are more thorough than I'd be able to do with my own information.
It is a good policy though and a good reminder to be vigilant.
I do run background checks on a decent chunk of people though for various reasons. The practical limitations are that some states are way easier to do this in than others. It just depends on how they set up their system. I've run them regularly in four states around where I've lived, and only one state would I say is truly easy to do. The other three are all limited to specific counties so you have to check multiple times even just to cover the reasonable daily commute in one area. And unless you have an idea of where else the person lived previously, you can't check the whole state unless you want to do it about 50 times or so which is time consuming.
Then there's the fact that if you are just going off first and last name, there are a lot of other people out there with the same name many times. For common names you definitely need some more specific info like DOB, SSN, previous addresses, etc. If you're a little clever you can probably figure out what you need, but again it takes some time and effort.
The IBJJF style background check simplifies things and checks more thoroughly than you can through the free public sites available. So it makes sense to have that kind of policy in place.
There are sites out there like Spokeo that make things much easier, but they all require paid memberships. They're not particularly expensive, but I wouldn't expect normal people to be maintaining paid memberships to investigative sites like that. The average person doesn't even really know about Spokeo. I only do because it's common in my profession.