At least two of the contributors above have - shall we say - expert local knowledge, so let's not start slinging mud around the forum!
Low flying [to me] suggests unreasonably low; IFR aircraft are never below 2100' over Edinburgh City Centre - if they were, they'd be prosecuted.
The one part of the letter that was correct is that pilots who have been cleared for a visual approach DO choose their own approach path; subject of course to the notified noise abatement.
Aircraft from the south are NEVER vectored for a five-mile final by ATC (except those not in performance group A).