JDK wrote:
I just made it up for laffs.

I don't have any evidence personally. However my good friend the late Robert Rudhall, author of the two books on the type, as well as well-known BoB film authorities Gary Brown and Peter Arnold knew of the story and regard it, IIRC, as reliable. Peter or Gary may be able to elaborate. I'll ask them.
I've never seen any pics myself.
I cannot confirm the story.
Aircraft for the Battle of Britain film UK element were gathered to RAF Henlow at the latter end of 1967 and through in to 1968. Here major restoration work to fly on three early Spitfires was undertaken together with 'Markaddie' conversions and assessment of German and Spanish aircraft. This work under the direction of Ron Boorman and Simpson Aero Services
I visited regularly over this period to monitor the incoming Spitfires for confirmation of their true identities.
There was certainly talk initially of the Ju87 being considered restorable to flight for the film and it was surveyed. The task in the time frame would have been enormous with the available resource and budget. That survey may have involved a brief run of the engine.
Keith Hamshere a unit stills photographer was tasked with taking test shots with grade scale of all the participating aircraft types, on the ground with their tails elevated to flying attitude to asses light level and behaviour prior to aerial photography. This was done in Tablada in Spain, Duxford for the Spitfires post the hangar collapse...but also on the Ju87 at Henlow. These latter shots show the aircraft still with the white rudder which JDK will confirm is pre film livery.
That the Ju87 was photographed elevated shows clear intent that flying was on the cards in the early days.
It would seem that plans for the Ju87 were changing quite fast. My shot here at Henlow shows that the it has lost its white rudder and acquired R+I markings and is in process of plaster moulds being taken for full size replication. This was later eclipsed in favour of using converted Proctor aircraft to succumb eventually to settling for just large full scale models.
By 18 April 1968 the Stuka hand been further repainted for a press rollout at Henlow.
So at least three liveries at Henlow...but no shots of the engine running I am afraid.
PeterA