Obviously, there are some Filipinos who have Spanish blood, just like in any culture. But do most Filipinos actually think that the Spanish blood is rampant among the population?
I think the notion is based on the fact that just because they have a Spanish last name, they assume their lineage is full of Spanish blood. Which is so untrue. The fact is, the vast majority of Filipinos have no Spanish blood in them. That's why almost all of them look like the indigenous people of Indonesia, Thailand, etc.
A lot of these claims are based on racial and social stigmas as well. Some Filipinos think that having Spanish blood makes them better than the Filipinos who don't. And they based this on looks. Which is hilarious. The thing is, the difference in looks is more attributed to the rampant Chinese blood among the culture. That's why some Filipinos are more lighter than others.
The main influence the Spanish had on the Philippines is not from them skeeting on the indigenous population, it's actually from them pillaging and destroying the native culture that existed in the Philippines before they came along, hence the Catholic religion, small similarities in language, and the name Philippines (which is in honor of the Spanish king at the time King Philip). The reason a lot of Filipinos have Spanish last names is simliar to why black people in America have white last names, the "oppressors" imposed their will on them and "branded" them with their last names.
So next time a Filipino tells you they're part Spanish, just give them the Bert stare.