Since it takes a certain unflappability to remain cool when you have been beaten over the head by a rule book, Gregory's reluctance to present himself for interrogation following Aston Villa's 3-1 defeat by Arsenal was understandable.
How could he speak truthfully about the incident that, more or less, put paid to Villa's stubborn resistance without treading on Elleray's toes and incurring the wrath of officialdom?
It was like this. Shortly before Julian Joachim had given them the lead after 44 minutes and David Suker's prompt equaliser, Villa had to consider the possible loss of their goalkeeper David James through the recurrence of an injury to his right knee.
Because James could no longer kick a dead ball, or out of his hands, sending him out for the second half may have been loose thinking on Gregory's part, but it did not deserve the punishment brought about by Elleray's obsession with the letter of the law.
Just four minutes after the interval, the ball safely gathered, James was left with only his hands for propulsion and no reachable target. Villa's defenders were at fault in this, but it did not excuse Elleray's pompous response to the goalkeeper's confusion.
Immediately, Elleray awarded an indirect free-kick for time wasting that left Villa to defend an assault on their goal from only nine yards.
Bergkamp's tap was blasted through Villa's surge from the line (the effect of Arsenal's illegally barging attackers escaped the attention of Elleray and his assistants) by Suker, and that was it for Villa.
James gave way to Peter Enckelman, who performed well enough to make you wonder why Villa took a risk with James' fitness, and, although Arsenal did not score again until Nwankwo Kanu got through eight minutes from time, they were comfortable winners.
Perhaps the issue of Elleray's refereeing, his pretty obvious rejection of the ethos that football matches are best served by a spirit of cooperation, can be defined by comparison with another schoolteacher referee, Ken Aston, who, when big in the game, was once described as a man among boys and a boy among men.
A word in James's ear would have sufficed on Saturday. Instead, Elleray behaved in the manner of a traffic policeman refusing to accept that a flat tyre absolves a motorist from causing an obstruction.
However, even before Villa were hit by the injury to James and the subsequent departure of Dion Dublin, they never looked like team capable of proving that second in the Premiership was not a false position. Using five men in midfield to counter Arsenal's technical superiority in that department, they rarely progressed beyond the half-way line with any of the purpose needed to unsettle a hugely experienced rearguard.
Certainly, they had nobody with the occasional wit of Bergkamp, who is travelling by road for the Champions' League game in Florence this week, or an attacker with Suker's predatory instinct.
Whether or not the Croatian proves to be more than an adequate replacement for Anelka remains to be seen, but he may prove to be a more consistent finisher than the introverted young Frenchman.
In describing Suker as a "box player", the Arsenal manager Arsene Wenger drew a comparison with Ian Wright, not only for his surges on goal but in communication with the audience. This leaves Wenger to accommodate the remarkable Kanu. The Nigerian's touch is sublime and his strength on the ball quite astonishing for one so slim.
A combination of both qualities further endeared Kanu to Arsenal's supporters. Holding off a powerful challenge, he found Ray Parlour and then got on the end of Marc Overmars' pass to complete Villa's destruction. As for Elleray, he probably thinks that he is a man of the times who is making a mark on the times that the times are better for.
Goals: Joachim (44) 0-1; Suker (45) 1-1; Suker (49) 2-1; Kanu (82) 3- 1.
Arsenal (4-4-2): Manninger; Dixon, Keown, Adams, Winterburn, Parlour, Vieira, Grimandi, Overmars (Henry, 83), Bergkamp (Kanu, 76), Suker (Silvinho, 69). Substitutes not used: Vivas, Lukic (gk).
Aston Villa (3-5-2): James (Enckelman, 52); Ehiogu, Southgate, Calderwood, Delaney, Merson, Taylor, Hendrie (Thompson, 63), Wright, Joachim, Dublin (Vassell, 71). Substitutes not used: Boateng, Samuel.
Referee: David Elleray (Harrow-on-the-Hill). Bookings: Arsenal: Winterburn, Grimandi. Aston Villa: Ehiogu, Taylor, Merson, Delaney.
Man of the match: Suker.