I have absolutely no specialist knowledge and actually agree with the previous answer... except...
How will you deal with the solicitor claiming his client told you she had changed her mind about going down the aisle to Beyonce's 'Single Lady' and wanted 'March to the scaffold' from Symphonie Fantastique instead? The WHOLE WEDDING was RUINED!
If you had insurance you'd avoid a lot of hassle.
I am not a Lawyer, but as I understand the situation, Public Liability Insurance would not provide any cover if you were to 'ruin' the wedding by playing the wrong music, or even if you were to play the right music badly. That would be a Contract matter.
However, if you were to play so badly, and/or so loudly that you caused a crush at the exit doors you might well be liable for the injuries caused.
Public Liability Insurance exists to compensate 'third parties' in the event of damage or injury caused by the acts or omissions of the Insured. Public Liability Insurance is increasingly being expected of 'outside contractors' by all manner of organisations, and especially government departments and local authorities, which I suspect is why the box has been ticked against your name.
As an example, I occasionally work for a large defence contractor at a site in Plymouth. I am not even allowed to attend a meeting there without proving, in advance, that I have £10 million PL Insurance!
For my sins, I am also Treasurer of our church 'Friends' organisation, which organises regular visits to places of interest, social events and so forth. All of the venues and coach firms involved have their own PLI, so in theory the Friends probably doesn't need its own cover. However, given the present claim culture it was decided that the Friends should stump up the £180 per year required, which would at least cover the cost of defending the Friends against a Vexatious Litigant should the situation arise. I suspect this is the stance of the OP's Clients.
However, in answer to the OP's direct question, an injury occurred at our local church when the Organist accidentally elbowed a copy of Complete Mission Praise from the ledge behind him (whilst turning around to look at the Priest), sending it flying down to the Quire around six feet below where it hit an elderly lady.
In the event no claim was made, but if the Organist was held to be an 'Outside Contractor' (rather than an 'Employee of the church') then presumably he or she could have been liable for any damages if this was not covered by the Church's insurance?