The person saying it depends why you're vegan is absolutely correct. I'm vegan primarily to boycott 'the industry' (its cruelty, its negative environmental impact, its general corruption; not individual farmers or workers within it or even the product itself) and only secondly for my own health. It's what happens to animal products during production and processing within the industry (industrialized farming) that contaminates them and makes them unhealthy, or not especially healthy, since there are no guarantees, for consumption.
so, I'd ask ~
How many chicken does she own? Five or six? Around twenty? Or, hundreds? Is she an actual producer, a farmer? If she's a farmer, is she independent or on contract with a big business? Is she organic?
Since I know she treats them well, as you say, if she owns less than twenty and cares for and feeds them organically OR is an independent farmer and cares for and feeds them organically, I'd eat the eggs. If it was meat or dairy (are eggs dairy? Not sure, but I mean milk products) I wouldn't make the exception. I'd love to care for chickens someday when I have the land, and would definitely eat the eggs they'd provided me.
If they meet my above criteria and you still don't feel right about eating them, be as sensitive as you can when you tell her about how eggs are processed on an industrial scale. Tell her about factory egg production. You don't even need to explain why you're against it at this point. Tell her her's *are* an exception, and you do appreciate the way she treats her chickens, but that eating them will get you wanting more and you never want to want to buy them from the grocery store.
If they don't meet it, e.g they're not organic, or she is on contract with a big, corrupt and destructive ruling production company (Hickman's, Dixie, Eggland's Best) that's why.
At the end of the conversation, no matter how it goes, tell her you love her. :-)
Thank you for being vegan.
Best of luck!! x