I'm sure I read somewhere in the past that it was a hang over from a previous rights agreement that saw the European Cup final - as it was - alternate between the BBC and ITV. The BBC had shown the last European Cup final in 1992, presumably the agreement for the final went to 1994, even as ITV had the rights for the new Champions League from 1993.
Yes, that does appear to be the case. For a while I wondered if ITV might have sub-licenced the match to the Beeb because ITV had shown Arsenal in the Cup Winners' Cup Final the previous week and they didn't want to show live football two weeks running, but as you say, it appears to be because the European Cup Final was still sold separately.
In those days the coverage of the Champions League was pretty ad hoc, that season after Man U had gone out in the early rounds I don't think ITV showed another live game from the competition, and only showed highlights, concentrating instead on Arsenal in the Cup Winners' Cup. It was in 1995/96 when the broadcasters were obliged to show a live game from every round of the competition regardless of whether their nation still had a team in it, hence ITV had to show Ajax vs Panathinaikos live in 1996, and I remember Chris Evans on Radio 1 the next morning wondering why they'd shown it.
Indeed, brilliant site it is too, the best and most complete guide to pre-Premier League football anywhere on the internet. One particularly interesting bit relates to the 1989 European Cup Final in Barcelona which nearly wasn't shown anywhere as Spanish TV were on strike, though at the last minute they allowed it to be filmed as long as it wasn't shown in Spain, so a crew from Italian TV flew in and did it, I know there was a clip on YouTube of Martin Tyler apologising for the rather ragged coverage in commentary.
ITV definitely showed the 1986 final between Barcelona and Steaua București. It was an atrocious match that ended goalless. Brian Moore and Kevin Keegan commentated on it and in later years would mention how bad a match it was.
I also remember Danny Baker talking about how the Sunday after, the same crew who'd covered that match then covered a Sunday league match for his series The Game about Sunday football, and at the end they told him the game was a million times better. He talked about that on Fantasy Football and on one of the videos there's a clip where he says that at one point the referee walked up to the camera to explain why he'd just sent off a player, in rather too graphic language to broadcast.
As the site points out, they lost the line to the commentators halfway through and Peter Brackley had to pick it up from London (the exact opposite happened a few weeks later in the World Cup, where the line to Peter Brackley went down and Brian Moore picked it up from London). It also points out that to get the season finished early for the World Cup, all three European finals were played within a week, the Uefa Cup Final first leg on Wednesday, the Cup Winner's Cup Final on Friday, the second leg of the Uefa Cup final on Tuesday and then the European Cup Final the following evening.