It should be July 4, some say, because on June 12 some 115 years ago we were really not yet independent.
My take: it is from the day the last American military force pulled out from the Philippines some 20 years ago. Here's a good piece that I can recommend.
I remember Pres. Cory marching to the Senate on a rainy day just to ask the Philippine Senate not to end the treaty which allowed US military forces on Philippine soil. It was one of the grand moments of the Senate, I must say.
I also remember Richard Gordon, many others, but mostly Gordon, ranting and warning about the end of the Philippines with the departure of the Americans. No such thing happened. In fact Gordon and his volunteers kept Subic floating. Gordon was wrong on that account but he and his volunteers also proved that we do not have to rely on others to prop us up. I salute Gordon and his volunteers for that.
Altho the Americans gave us "independence", it came with many pre-conditions. See this article in Wikipedia for the many "strings attached".
So, we have only been independent for 20 years yet. We have done a lot in those years. We can do more in the next. Looking forward to it.
Until then let's sing the Philippine National Anthem: