This question might be too board to answer as-is as tax codes differ state to state and tax law is extremely complex. Here are some points of thought about the claim.
Pulling up the original land grant/patent the property my parents own, you can plainly see that "released from all interests, taxation, and control of the state to all owners, heirs, or assignees forever" language is not present. This does not mean it doesn't exist but keep in mind that legal jargon does get copied around a bit in my experience, building upon past examples.
PDF of Land Patent from the Federal Government of Louisiana Purchase
Look for more here (I check a handful couldn't find that phrasing):
The closest phrasing is, "together with all the rights and privileges, immunities and appurtenances of whatsoever nature... name ... and to his heirs and assigns forever." Note that is does not simply say rights but in-fact include privileges that the state or federal government may bestow to the holder of the deed or title. This implies that an owner may not have carte blanche rights over their land. They have the rights bestowed by the government, which might not be the philosophical 'all-rights possible'.
The frequency of the exact phrasing of the land patent really isn't going to be what wins or breaks the case of property tax responsibility. There are some other problems with the claim that seem more damning.
Missouri real property tax code about what is to be taxed is very simple:
137.075. Every person owning or holding real property or tangible personal property on the first day of January, including all such property purchased on that day, shall be liable for taxes thereon during the same calendar year.
There are no provisions or exceptions.
A major point from my Urban Planning Law 101. It is not uncommon that in some areas of the US, that there are land covenants, I believe that they are extremely common in Texas. These covenants can go back to the beginning when the land was patented. So, unsurprisingly there are many things in covenants that are completely illegal today; usually these are in the form of racial restrictions on ownership. Of course today, these are not followed, there is a law saying this covenant is null and void. Covenants are not laws in of themselves, Texas cannot enforce the covenant just because it was there before the state of Texas outlawed racial discrimination.
Looking to a land patent, with the phrase "released from all interests, taxation, and control of the state to all owners, heirs, or assignees forever". Logically, the same could be held true here. This clause may have been true at the time of the document's draft but since then overturned by the state legislature passing new laws. Land patents are not laws and are subject to current laws, if they conflict with the law that clause probably will struck.
Minor note: A reasonable judge isn't going to take an aerial photograph with a consumer grade GPS points, and your word that property in question is actually your property. You are going to need a professional survey, and go back through years of land deeds to be sure that what your are show is actually your property. I work in local government in community development, mistakes about property boundaries are all too common and I end up telling owners to hire a surveyor.
A couple things from the second site.
We have a Constitutional right to own property.
From what I know and can read. The Constitution says very little about citizens owning property other than the 'taking clause' found in 5 and 14. And that reads to me as we have the right not to have it taken away unjustly not to own it.
There is no due process in an Eviction
This is all wrong. The due process is the eviction. That is the reason the sheriff shows up with a court order to vacate the property. In Missouri the evicted individuals have the chance to show up in court and plead their case before the judge issues the eviction.
If you don't pay your property taxes, the county sue you for the taxes. The judgement is the auction of your personal property to settle your debt with the county. Guess what? This judgement took place in court, through due process and now you are being evicted and having your stuff auctioned. Whether the green-ink brigade recognises the power of the state or not doesn't matter to the state; they will come to collect and any legal claim you have to the property will not stand in any subsequent case.
The author of the second site even admits:
Now, I have NO IDEA if this is true, or if this method would apply in other states.
Is it possible to avoid paying property taxes? I don't want to say with an absolute no, but there is many years of legal precedence that says otherwise. Best bet is to hire a real estate / tax law lawyer but I wouldn't expect to get very far on the merits of your case.
Otherwise I remain extremely skeptical of the site's advice, it tingles my 'woo detector' as freeman / sovereign citizen / green-ink pseudo-legal witchcraft.
In the meantime, I would continue to pay my property taxes...