I am licensed in Nevada, but this answer should apply in Texas as well.
Your false statement has nothing to do with whether or not the truck driver should pay for the damages to the car. Nor does it have anything to do with whether or not the truck driver should compensate you and/or your son for any physical injuries he may have been unfortunate to have suffered.
If your son was a permissive user, then your mother's insurance could pay for any uncompensated personal injury or property damages resulting from the accident depending on the available coverage. Again, your false statements have nothing to do with this unless your son is specifically excluded from driving the car. If so, then your statement could be considered attempted insurance fraud. But, I think the quick (and proper) retraction of the statement should clear up that issue.
Hope this helps.
/s Donald Kudler
You need to report the accident to your insurance company and open an uninsured motorist claim. If your son sustained injuries, he should consult a personal injury attorney. I would be happy to discuss this with you. My number is 512-472-8318.