I really don't think they're "pink" eggs. I think they're the shade of brown that, when added to the blue egg gene, gives you the typical greenish EE shade. There aren't white, brown, pink, blue, green, and olive egg genes. There are white, brown (with the amount of brown laid down giving you the shade), and blue. Blue + those varying shades of brown gives you the green or olive eggs. Remove the blue and you're back to your various shades of brown.
The blue egg gene is very, very closely linked to the pea comb gene. They're almost always inherited together. That's why when you get a single-combed offspring of an EE or an Ameraucana it almost always lays brown. But, a very small percent of the time, the pea comb is inherited and the blue egg gene doesn't come along with it, so you get a visual EE without the egg color.
I agree that we can't just call any mutt, or any mutt with partridge/wild coloring, an EE. They're a very specific type of bird with a predictable body type, comb, muff/beard, and egg color. Every other breed has a visual standard - i.e., a Leghorn born with a walnut comb wouldn't be a Leghorn anymore, or a BCM that consistently lays an under-4 egg isn't a BCM anymore - so I think once it stops looking or laying like an EE we can stop calling it an EE.