If your level 69, and you do a quest, lets say one that give gold, and one green item, You will get exp, gold, and the green item.
However if you are level 70, You wont get exp, but rather more gold. And the green item to boot.
Also, to the main post,
If a level 60, without the BC, keep doing quests that gave him exp, whould he get to 61? he whould not. Same way a level 70, could not get to level 71.