The PR department said "may"
And therein lies the issue. It "may" be criminal dependent on the wording in the Terrorism Act 2006 if you regard You Tube or any other media site on which the video has been made available as passive and that therefore the act of transmission is initiated by the person who clicks on the play button for the video. As the police wish to stop people viewing this (and not necessarily for criminal purposes but for the protection of the public in general) then they may "choose" to interpret the law in such a way. As the PR wonk said, it is all down to interpretation.
It is important to remember that the police are not only required to respond to criminal incidents but to act in such a way as to protect the general public from the possibility of crime. By interpreting the law in a particular fashion they may well be able to restrict or prevent people from doing something criminal. For example by planting the suggestion that watching a certain type of video may be illegal they may be able to prevent young knobheads from circulating the link as a joke or windup or even threat ("grass us up and this is what will happen to you") which is according to the Act a crime. One only has to look on line at the idiots who pose with guns or the money from drug deals to see some of the idiots that the police have to contend with or even worse the drunks who piss on war memorials while their mates film them.
I am not friend to the police having seen members of my family suffer from their stupidity and desperate attempts to justify large sums on investigating non-crimes but at the end of the day they are a very thin line responsible for protecting a lot of people and have often given their lives in undertaking that duty and it appears to me that they may, given a more favourable view of their actions be seen as trying to prevent crime by implying that an innocent act could be interpreted as a crime.