The income tax rate in Philippines is around 32%. It is close to the rate within the United States. So if someone renounce his citizenship, I am not sure how much he is going to gain in terms of savings. And also, once you renounce your American passport, it will be extremely difficult to get it back at a later point. A Filipino passport is useless for international travel.
Most likely, the majority of the people renouncing are ex-pats who already live overseas and are being double taxed by virtue of being American citizens. There is limited benefit to emigrating to avoid American taxes as the savings are probably negligible and the cost of giving up American citizenship is high, but in instances where someone is already gone, it makes a lot more sense.