Brit,
Sorry I was not there to back you up, but as a horticulturist I have to look at the soil in which the palms were growing. If I were to take a soil sample I assume I would see sand. Hmmmm. Anyway, even with a 2-ton truck I do not think there would be any compaction of the root zone that would cause ANY anaerobic, anoxic, or hypoxic conditions. There may be some stress to the roots, however seeing they survive in such an environment (hurricane winds, salt spray, salty water, high temps, lack of irrigation water and only precipitation as a source of water) I think they would survive. Also, unless you drove within a foot of the palms, there would have been NO disturbance to the roots as they have a small root zone (think of those HUGE berlapped palms with a small root ball).
Now, if the soil consists of a sandy loam or clay loam then your vehicle traversing the ground would cause a reduction in the pore space found in the soil; also known as compaction. This would reduce the amount of oxygen exchange in the root system and may cause a reduction in plant vigor.
I think it would be safe to say some fertilizer would have compensated any soil compaction you may have caused (poo = high nitrogen). In other words sht on her lawn.
BTW: I will speak with a friend of mine at school, he works for Hines Horticulture (grower) working the Home Depot garden center. He knows the retails of all the plants there, I will check to see if she overpaid.