OK, ignoring all the noise, and in absence of the OP actually bothering to tell us what he was charged with.
As pointed out CISCO's answer is wrong because the law is different in TEXAS. It's also wrong because even if this had happened in Seattle, he posts a completely irrelevant statute. Speeding enforcement was not the issue here.
IN TEXAS:
There is no requirement to have a drivers license on private property. Of course, if he told the police he had driven there, they may make a cause that he had operated on the highways without it. There's nothing that precludes you from being issued a ticket on private property for an offense that occurred elsewhere.
HOWEVER, there's the rules for property damage accidents. That includes giving the insurance info to the other driver AND showing your drivers license. If you don't have it to show, you can be held in violation of that section (in this case, there is no requirement that this be on the public roads).
I suspect however he was charger with 521.021 which will be dismissed if you show you did have the license (based on what the police officer said).
Now for the other charge: 545.415 Backing a vehicle does not seem to be limited to public highways, so yes you can get it in the parking lot.
The decisions on traffic enforcement on private property are a little varied in Texas, but the body is against you on this. The statutes talk about what people can and can't do with private roads, parking lots are not enumerated, but ones that are not residential in nature or private (ie., gated) generally will be subject to traffic law enforcement.