The how do they know it's my cat excuse is merely a get-out to force the burden of proof on the victim and avoid responsibility. Hardly self righteous to realise folk get to the end of their tether, need the issue sorted, but don't wish the stress of a row/confrontation with the neighbour. Where the returned gift was left was unfortunate but clearly it was meant to be noticed and understood as something causing anger/frustration.
All cat owners should either train their pets to go in a specific area of their own garden or ic that fails accept that the cat isn't that bright and should be an indoor cat. Bit unfair on older cats that suddenly get curtailed though.