Is argument-dependent lookup the only way val() can be found?
Yes, it is the only way. To quote the holy standard at [namespace.memdef]/3:
If a friend declaration in a non-local class first declares a class,
function, class template or function template the friend is a member
of the innermost enclosing namespace. The friend declaration does not
by itself make the name visible to unqualified lookup or qualified lookup.
So while val is a member of foo, it’s not visible to lookup from the friend declaration alone. An out of class definition (which is also a declaration) is required to make it visible. For an inline definition (and no out-of-class declaration) it means ADL is the only way to call the function.
As an added bonus, C++ did once have a concept of “friend name injection”. That however has been removed, and the rules for ADL adjusted as a replacement. A more detailed overview can be found in WG21 paper N0777 (pdf).