Can a school know if you have a degree, if you don't tell them?

[EDUxplorer]

I've seen that some universities will not accept a student into an under-grad program if they already hold a Bachelor's degree. I've also seen some grad-level programs that state they will not accept if you have a similar grad degree or working on one that could be similar.

Example:
https://extension.harvard.edu/registrati...ligibility

My question is this:
Can the school verify or know that you have a degree or are enrolled at another school for a degree if you don't report it to them and did not use financial aid?

I ask because what if a student has a Bachelor's degree from an NA school but would like to get one from an RA school? Could that RA school check and see if they already have one, then turn them down? What if a student has a Masters of Information Technology focused on Networking but wants a Masters in Cyber Security?

Food for thought in my head...