PROVED
This has been solved in the affirmative.
Let $A\subseteq \mathbb{N}$ be a basis of order $r$. Must the set of integers representable as the sum of exactly $r$ distinct elements from $A$ have positive lower density?
Erdős and Graham also ask whether if the set of integers which are the sum of $r$ elements from $A$ has positive upper density then must the set of integers representable as the sum of exactly $r$ distinct elements have positive upper density?
The answer to both questions is yes, as proved by Hegyvári, Hennecart, and Plagne
[HHP03].
Additional thanks to: Boris Alexeev, Wouter van Doorn, and Mehtaab Sawhney
