Is it just me, or is "The Midnight Ride of Paul Revere" meant to be sung to the tune of Greensleeves?

I doubt that the author "meant" for it to be sung to that tune, but it's not exactly a "coincidence" either. There's a finite number of meters that metrical poetry and metrical songs are written in, and any poem written in a particular meter that can be sung to a particular tune (like Greensleeves) can be replaced by any other poem in that same meter (like Paul Revere).

The best-known example of this phenomenon is the tune of "Gilligan's Island," whose words can be replaced by lots of other poems or song lyrics, such as "Amazing Grace," "Casey at the Bat," many poems by Emily Dickinson, etc. That's because it's in "ballad meter" or "common meter" (a name that suggests just how many songs and poems are written in that meter).

it's just you. don't try it on public transport if you have any regard for your fellow riders.

If you like singing do it.

I've tried and it doesn't work for me.

There is no historical documents regarding this theory.

You can claim credit for this amazing idea by informing

The NYC Poetry Foundation.

It's a coincidence in the way the metre and tempo can match. FWIW, it's only a poem and not historical fact.

It may inadvertently share the rhythm, but there isn't a known correlation.