Consider his official Independence Day statement.
Human life being mortal, surely some people died on July 4, 1776. Some extraordinary men also lost their lives on July 4, 1996, to avenge the hundreds of millions killed the two days prior by aliens.
But ID4 is just a movie, and July 4, 1776, is generally celebrated as the anniversary of the signing of the Declaration of Independence, not the beginning of hostilities in the Revolutionary War, which began about a year earlier when ... oh how about we let Sarah Palin explain it.
H/T: Chris Geidner