An added question to this - how typical was the observation I heard (and was it likely accurate)?

I heard second-hand from someone in Reno, Nevada who was on the local draft board during the time of the lottery. He was a wealthy attorney who was the chairman for major political campaigns in the state. He said that although the lottery seemed fair, he was not about to let the rich kids go to the war, so the board always filled their quota from the poorer neighborhoods. They used the lottery system, but they sidestepped children of "better" families.

I understand that the draft was still implemented by local boards, leaving this sort of "adjustment" in the hands of the powerful.

Was this likely accurate and was it prevalent?

As it's name suggests, the lottery was just that, a lottery. Except most people did not want to have their number picked in this one. Every day of the year was assigned a number (01-365). When troops were needed, numbers would randomly be picked out of the bunch and men of drafting age born on the chosen date would be expected to show up. It's because they used birth dates that noting who was missing (draft dodging) was an easy task. It also gave them an easy way to measure how many troops they could expect from a specific date. As for the second part of your question, I do not know. I would suggest that the process itself was not designed unfairly against poorer citizens, but cases of sons of a wealthy family dodging the draft without penalty were almost certainly an occurrence. That was the case during the Civil War when the US first used the draft.