That explanation does give the right idea, y not.
However, the word dhamma should not be attributed to Vedic teachings. It has origins in the previous Buddha, Buddha Kassapa (and, of course, to even earlier Buddhas). All Buddhas teach the same Buddha Dhamma.
I have touched on that in several posts. I mentioned that again in #5 in the introduction to the new series of posts “Buddhahood Controversies – Introduction.”
– I will write more on that in upcoming posts in that series.
Dhamma means “to bear.”
– Everything in this world arises due to dhammā (created by the mind.) Buddha’s teachings about how that happens is called “Buddha Dhamma.” See, “Dhammā, Kamma, Saṅkhāra, Mind – Critical Connections.”
– More clarification at, “Ye Dhammā Hetuppabhavā.. and Yam Kiñci Samudaya Dhammam..“