There is a lesson to be learned from this and not least at Hibernian, where the industrious Dempster will attempt to turn around the woefully under-performing club from June. The switch could hurt Motherwell, but there was only bonhommie being shown towards the chief executive, both outside and inside the stadium.
One of the club's many initiatives ensured there was a much bigger crowd than usual to witness the 2-1 win over St Johnstone which took Motherwell to within a point of Aberdeen in the chase to finish second behind Celtic. Local schoolchildren swelled the attendance to more than 7000 for a fixture which might normally attract only half that number.
The fans, young and old, enjoyed an entertaining game in which the home side dominated the first half and the visitors the second. Lionel Ainsworth's opener was a gift for Motherwell, the midfielder intending to send an inviting cross into the box but instead being rewarded with a goal as his effort deceived goalkeeper Alan Mannus.
The Englishman, to his credit, made no attempt to disguise the nature of his attempt. "If you buy a lottery ticket you never know," said Ainsworth. "I just wanted to put it in the box and fortunately it's gone in - it's probably the bit of luck you need."
If the opening goal was a surprise, what turned out to be Motherwell's winner - after Dave Mackay had quickly equalised for St Johnstone - was shrouded in confusion. Tommy Wright, the Perth side's manager, was, like his players, adamant that Mackay was fouled - and therefore not marking goalscorer Stephen McManus - as Iain Vigurs delivered a free-kick into the box.
Referee Kevin Clancy was having none of that but had to make a decision on whether the ball had crossed the line before Mackay's central defensive partner Steven Anderson handled it clear. As Clancy hesitated Motherwell manager Stuart McCall was not alone in thinking the outcome would be a red card for Anderson and a penalty, but assistant referee Andrew McWilliam's view was that the goal stood.
"The ball was already over the line so I put my arm on it," Anderson confirmed. "I was shouting it was a goal and the linesman knew. I got booked for unsportsmanlike behaviour - I don't know why if the ball was over the line."
At that stage, 10 minutes from the interval, a comfortable win for the home side looked probable, but the visitors were perhaps energised by the incident and their performance in the second half dispelled any notion that they are saving themselves for the William Hill Scottish Cup final.
That may change in their two remaining league games against Celtic and Inverness Caledonian Thistle, as the defeat realistically ends any chance of pipping Dundee United for fourth place in the league. Frazer Wright was rested by his namesake on Saturday and others may follow over the next six days.
"The older boys might get rested, but I'd rather play right through," said Anderson, who had a lengthy injury at the end of last year. "As a centre-half your timing goes if you're not playing as many games."
St Johnstone need to win the cup final, against United, to play in Europe next season but Motherwell remain firmly on course for another tilt at continental football - they now need just one more point from their remaining games against Inverness and Aberdeen. The latter meeting, scheduled next Sunday at Pittodrie, is also shaping up as the game which will decide who finishes second in the Premiership.
Ainsworth's goal was his 11th of the season, his best return in a career not noted for its peaks. He has flourished since arriving on loan from Rotherham and, whether that speaks more for the standard of Scottish football or the restorative powers of Motherwell, he has certainly paid his way this season.