It does look pretty clear but there's one caveat.
A disk that is pinned by an enemy disk and is also pinning another enemy disk itself, is an embattled disk,
Is pretty clear.
as it is both an attacker and a defender in separate engagements
Is the point that is being contended. Even if an engagement is resolved, the disk still met that criteria.
That said, the point that disks should not need to have a memory is a good one though even as it stands they do to some extent (you must remember whether engagements were created from the results of other engagements or were there at the start of melee phase). I expect the official ruling to run along the lines of the consensus given here.