WHEN IS A COUSIN WHO ISN'T A COUSIN A COUSIN AFTER ALL?

I was back at Mt Vernon Cemetery here in Abington the other day taking
pictures again in my project of photographing the entire cemetery when I
came across this monument:

The inscription reads:
Lewis Ellingwood Noyes
July 3 1923.
Sept.  15 1896.
Servant of God, well done.

Well, my first thought was this must be another Ellingwood cousin!  Last night
I checked online, reasoning that Lewis probably had Ellingwood grandparents
or ancestors, hence the middle name. But I found none. Lewis Ellingwood Noyes
was not an Ellingwood cousin.

But... his mother was named Olive Edson and her maternal grandmother was  a
Sarah Packard. My 4x great grandmother through Florilla Dunham was Cynthia
Packard and one of her ancestors was Susannah Edson. It turns out that Lewis
Ellingwood Packard is a cousin after all, but not through my Ellingwood line.
He's my 5th cousin 5x removed through our Packard and Edson ancestors.