I'm in the first camp. I think that foreign key relationships should be modeled in the contextual model because they are there for a reason. They represent a real-world relationship, and that relationship should carry through to your conceptual model. If this is not the case I would argue that "you're doing it wrong" ;-)
I'm sure there are exceptions to that, but I'm no stranger to database design and data-driven applications, and I've never created a foreign key that didn't have a purpose. Definitely not one that existed only to satisfy the database and be discarded elsewhere in my architecture.
Do you perhaps have an example you can share with us when it's preferable to ignore the fact that there's a foreign key association in the database? What do you do about error-handling in that case, and how is it preferable to catching the foreign key error raised by EF?