You're not wrong in terms of your conclusion that UT and A&M have deep pockets, but it's worth clarifying that UT is not a land grant school, though Texas A&M is, along with A&M Prairie View. And the deep pockets have nothing to do with being a land grant school, a status whose origins go back to the federal government donating grants of land for state universities first during the Civil War era (when A&M was established), with a second wave in the 1890s (when Prairie View was founded).
The reason the UT and A&M schools have deep pockets is the oil and gas revenues trust that contributes over $1b per year to the Texas state schools. That, not an act of generosity from the federal government 150 years ago, is why they're so rich. Just ask poor land grant schools like Oregon State and Washington State - being a land grant is no guarantee of deep pockets, and usually quite the opposite.