The assumption both you and AnyList are making is that an email is "THE obvious choice". From a user experience perspective perhaps this "global sharing identifier" should be defined by them.

You'll notice that different generations have different online behaviors. For some, email is their main id. For others, it's their phone number (they don't know most of their friends' e-mail, but know their phone). For others, it's either online handles or nothing at all - think about the device set up for grandma with her daily To Do list.

Of course, having this approach would add some upfront dev work to them but allow them to navigate this much easier later on. And for anyone starting to develop their new app/site/product thinking about this early on can reduce a lot of future headaches.