This provision would apparently protect the landowner from criminal prosecution under this law if all four of these provisions were met. (1) Persons leasing or renting land would not be permitted to foul that land and escape criminal charges unless the landowner had given them permission. (2) The waste contemplated must not be from a commercial operation. So if the land owner was hauling commercially-generated waste from his business in town out to his ranch for dumping, this would not be allowed. (3) The generation of non-commercial waste and the actual disposal could happen on different pieces of property, as long as both were owned by the same individual. (4) Any actual disposal couldn’t be for commercial purposes, defined at Section 365.011(3) as "the purpose of economic gain." I’ve heard more than one prosecutor say that disposal to avoid waste disposal fees would certainly be included under this definition. So if a person is dumping household waste generated on his own property on property he owns for some reason other than economic gain, the State Legislature apparently meant to protect this activity from criminal enforcement. Many officers find the "for commercial gain" issue is the easiest to address. After giving the appropriate warnings, the officer simply asks, "Did you dump that stuff to save money, or what?" But if all four of these provisions are met, the individual will probably escape prosecution for a criminal violation of THSC Chapter 365.

THSC Section 365.014 protects farmers from being prosecuted for illegal dumping under this law in some circumstances. It also protects those individuals that are dumped on through trickery (i.e., the dumper left trash hidden in among good materials and the receiving individual didn’t know this and was uncompensated). But the protection to farmers from prosecution for dumping under some circumstances is the most important of the several provisions in this section.   

Farmers who dump feed sacks and such items would be free from prosecution. Note that the law doesn’t require the dumping to be on the farmer’s own land, although few farmers in Texas would dump anything on a neighbor. Enforcement officers need to be sensitive to these two defenses when enforcing THSC Chapter 365.

Texas Water Code [TWC] Chapter 7(Subchapter E)
This law contains the bulk of Texas’ felony and specialized dumping statutes. Included are such things as dumping waste motor oil, lead-acid batteries, medical and hazardous waste, dumping that pollutes or threatens to pollute water, and dumping into the air of Texas through illegal burning. There are no defenses in this law to violators based on their ownership of the property where the dumping took place. For example, if someone dumps waste motor oil in violation of TWC Section 7.176, the fact that they did so on their own property is no statutory defense. TWC Section 7.523(c) does provide defenses to defendants who unknowingly purchased polluted land, provided that they meet specific tests showing due diligence specified in the statute. 

State Criminal Nuisance Laws
Note that there is no defense to violating the nuisance laws and local ordinances based on the fact that you own the land where you are committing the violation. The two primary nuisance abatement statutes in Texas, THSC Chapters 341 and 343, both contain provisions that would probably classify trash dumped just about anywhere, including on one's own property, as a nuisance. Although the penalties are small, the fact that these statutes both consider each day of an ongoing violation to be a separate offense give them sufficient punch to be useful where THSC Chapter 365 cannot be used and TWC Chapter 7 is not applicable. Where applicable local ordinances exist, they too may be a good way to deal with waste dumped on one's own land.

Civil Enforcement
Sometimes local governments can act civilly to stop illegal dumping on one’s own property in cases where criminal violations don’t exist. There are great reasons for civil enforcement, including the possibility of getting more parties involved in the cleanup and in keeping more of any civil penalties assessed in your jurisdiction. Under Texas Commission on Environmental Quality Rule 330 (30 Texas Administrative Code 330.7) a permit or other permission is generally need from the TCEQ before an individual can undertake any solid waste activity:

By removing the requirement for deed recordation of waste disposal on private land, the TCEQ has effectively eliminated any requirement for local records to be maintained of where the small private family dumps are located. A title search will no longer yield any affidavit providing public notice to new buyers of the property. Now when you dig the hole for the new swimming pool and hit a few tons of trash, you won’t be as able to sue the former owner for running a mini-dump without letting future buyers know about it by deed recordation. Since everything had been disposed in accordance with TCEQ's rules, perhaps the existence of the buried trash would not be a known environmental risk requiring disclosure by the seller.