When you make a bet preflop with the intention of isolating and/or protecting your hand, you have to make sure you don't give your opponent(s) good enough odds
to stay in. The 4bb + 1 per limper rule is just a general rule for people who can't calculate what odds they give their opponent when they raise.
3 people limp, you're on the button with AA and raise 4bbs.
Pot is 8.5bbs now. Any limper only has to put in 3 more bbs, and he's getting ~2.8:1 which is WAY too inviting. It doesn't sound like much, but NL is a game of implied odds, and that's exactly what you're laying in this hand. This is just a pot-sweetening bet and it's a terrible play with AA. You need to raise more to isolate the hand, aswell as protect it.
3 people limp, you're on the button with AA and, using the 4bb+1 per limper rule, you raise to 7bbs.
Now the pot is 11.5bbs, and 6bbs to call for any limper (or BB). Now they're not even getting 2:1, and you've protected your hand and gotten full value should anyone call.
Actually looking at it, the difference in odds isn't as much as I'd thought. To put it in perspective, you'd be much less inclined to call the second bet than the first with 78s, though, wouldn't you?