There is a big difference between an aircraft which crashed and one which was dumped.
In the UK(and UK Waters) ALL crashed military aircraft irrespective of nationality or date of loss are protected under the Protection of Military Remains Act 1986,under the act it is an offence for anyone to tamper with,damage,move,remove or unearth any part of a crashed military aircraft.
The USAF did indeed claim to have abandoned ownership of the remains of aircraft lost prior to 1961,however in the UK this makes no difference due to the 1986 PoMRA. Other Countries may also have similiar local laws which protect remains.
The US Navy's position is that if it ever belonged to them it remains Navy property.
With dumped aircraft,parts,equipment etc the ownership could rest with the landowner,but again there may be local laws/bylaws protecting the site,depending upon the location.