Nudels, I'm willing to be that you've got that TN law misinterpretted. Or whoever told you that information had it misinterpretted themselves. The wording your aluding to (if it's even there) probably says something about not detecting any historical site or object, blah, blah. And it may extend itself from the state level ALL the way down to ANY public land beneath that level: county and city too. The novice reader fails to understand that the key words are "historic site/object". They simply focus on the "extension to any commonwealth land blah blah", and think that means all public land is offlimits. Yup, even the local city modern school, or whatever. But if you read the law closely, you will see that the site needs to be DECLARED such a site, or an object has to be found and THEN be declared as such, so the site can then be labled as such, thereafter being in that level of protection. So basically, yes, you can't, in that/those states, go into protected momunents, active archie digs, etc.... But the wording in no way applies to ALL public land UNLESS they were ..... as they say in England .... "Scheduled" sites.
As far as your last question, on where to find a list of each state's laws, you can go to the FMDAC website, and follow the links to a state-by-state list they made. But be aware of a few things:
1) It would only apply to state land (like state parks) not "all" land,
2) the way they got their information was to simply send a letter to each state park's head office and ask. So depending on the way the person opening and reading that mail felt/interpretted it, is the type answer you would get. So for example: It's a given that in ANY state, a few of the state run parks would obviously be historic in nature. But a whole bunch of them probably aren't historic, nor would ever have cared or even thought of the issue. But rather than break each one out individually, they just give a blanket "no", or "ask at each kiosk you come to" etc...
For example: If you read the FMDAC's portion on CA, you might walk away downright discouraged. But what's wierd is, there are a lot of state parks (and ALL beaches) that you can detect here till you're blue in the face, and no one will ever say "boo" to you (as long as they're not obvious protected historic monument type places) But I suppose if you asked enough persons, and kept going high enough up the ladder, you would eventually find someone to tell you "no" (to address your pressing issue).