I've been lucky in not having any picking going on. I had thought of them rubbing against something, but there's nothing purple or even blue in color they could have gotten into. I thought about mould a bit ago, but the eggs hadn't been out there long (2 hours max) and the color doesn't rub or wash off.Have you looked to see if your hens have gotten their bootys stained with something?
A few of my gals who are just horrible meanies that like to pick on each other around the tail feathers, in an effort to stop them I used blu-kote to paint them and was hoping it might discourage their behavior. I kinda forgot about it until the purple spotted eggs started showing up in the nests. Sure enough just from them rubbing around on things they managed to stain the eggs.
Don't know if that is what is going on with your Freddie the Freeloader (love that name) and other gal but you might want to rule it out.
Good luck!
Now that I think about it, it's more the color of lavender project eggs, but I have none and Jazzy and the 2 RIR girls are hatchery stock.