If you want to go down this route then the US Independence Day only applies to the original 13 states which is totally stupid.
The 26th is just a random day in the calendar and as good as any other. It is not Invasion Day (that is today) and it is not the Founding of NSW Day.
Australian Independence Day is the really the 22 May 1856 when NSW's first full elected parliament sat. At this point we took over running things ourselves.
