The law says that there is no infringement of a literary, artistic or musical etc work if is included incidentally in another work. Furthermore there is no problem with showing, selling or broadcasting the second work if there was no infringement by virtue of the original recording (the second work). This much I'm sure you know. The key here is: what counts as incidental inclusion? The CDPA says something is not incidental if it is deliberately included, but that doesn't really help much. So turning to caselaw there are three relevant cases – strangely all involve footballers – which might help show how the courts view this topic. Unfortunately the decisions are split. The first case is Football Association Premier League Ltd v. QC Leisure 2008. QC Leisure broadcast certain football games in which an anthem was heard during the opening stages. The copyright in the anthem was owned by FAPL and they claimed that this broadcast of the music was an infringement. The judge found that as the broadcaster recorded the sound in the stadium via microphones in order to capture the atmosphere of the crowd, and as a result the sound quality of the music was patchy, this was incidental inclusion because the broadcaster did not appear to have set out to capture the music alone or in any quality, but rather that it was a by-product of recording the general sound of the match which included the crowd chanting, singing and so on.
The second case also involves FAPL. This time it's FAPL v. Panini UK Ltd and the case revolves around pictures of football players on collectors cards which were published by Panini. FAPL claimed infringement of their copyright in the FAPL emblem which was on the shirts of the players when they were photographed. In this case the judge applied the test of whether the presence of the emblem was important to the business of selling football cards. And he found that it was, since fans would expect the players to be in their official strip which included the FAPL emblem. As a result Panini were unable to rely on the incidental inclusion defence.
The third case – Fraser-Woodward v. BBC/Brighter Pictures Ltd – revolved around newspaper pictures of the Beckhams which were included in a TV documentary. BBC/Brighter Pictures claimed this was incidental inclusion as the camera panned over a number of newspaper and magazine articles about the Beckhams. Copyright in two specific pictures was held by Fraser-Woodward who claimed infringement. The judge held that one picture could reasonably be said to be incidentally included, whilst the other was featured more prominently and thus became the point of the shot, rather than something in the background or on the periphery. (In fact the whole claim was dismissed, despite the finding on this one photograph),
So having given you that background, how does that affect your situation? I can't say what a court would decide, but in my opinion the music seems pretty important to the overall performance of the skater. Or to put it another way, if the music wasn't recorded, would the film still have the same value in your documentary? Assuming the answer is that the music is important, you would find it hard to claim incidental inclusion, and if you don't want to run the risk of infringement, I think you need to approach this with a view to getting a licence to include the music. I am assuming that the venue for the skating will already have a licence to use the music for a public performance. If not, be careful not to drop them in it!
I think you need to approach is PRS for Music http://www.prsformusic.com
about a licence to use a composer's work, and Phonographic Performance Ltd http://www.ppluk.com
to use a recording of the music. Obviously if the composer of the music has been dead for over 70 years, you should not need the PRS licence. Be aware that both organisations have a fearsome reputation for extracting the most advantageous settlements for their respective clients, so you will need to make sure you get a licence which covers just your specific circumstances and not some off-the-shelf licence which covers far more than you need (and of course costs more!). If you feel they are being unfair in their proposed licensing fees, you can appeal the the Copyright Tribunal for arbitration. And incidentally if you do appeal to the tribunal you can still go ahead and record the performance while your case is considered although obviously you will have to pay some licence fee eventually.