This is correct. I am an aviation lawyer.
The right to make a claim for compensation under UK 261 belongs to each individual passenger. For administrative convenience the compensation has been paid to the lead booker, but they are acting in the capacity of representative of each person in the group.
This becomes clear if you consider what would happen if the airline did not pay and the passengers took the claim to court: the lead passenger could not make a claim for the whole sum, only his or her own £520. Each other passenger would have to claim in their own name.
The compensation amounts were set by the EU to represent a fixed sum which reflects the inconvenience suffered. The idea was that people could claim quickly and easily without having to produce documentary evidence of financial loss. (Originally, Regulation EC261/2004 only provided for fixed compensation for cancellation, not delay, but a European Court of Justice case called Sturgeon extended the right to delay claims in 2009. ) When the UK left the EU the legislation and historic case law were transposed wholesale into UK law and the Euro amounts were converted to GBP.
All passengers suffered the same inconvenience and this is entirely separate from the cost of the flight. As someone correctly said upthread, if your employer has paid for your flight you are still entitled to the compensation because you suffered the inconvenience. Claims can be made by children.
The wording of the airline’s agreement to pay should list the name of each claimant and will probably assume that the lead passenger is acting as agent for all the passengers. It should also request the lead passenger to sign a release confirming that no further claims will be pursued, but airlines can be quite lax with this sort of stuff.
It’s correct that the airline will not care how the lead booker distributes the money, but if there were ever to be litigation between the passengers I can guarantee you that a court would hold that the lead booker would have no right to keep the money or distribute it in any way other than £520 per passenger unless all parties agreed. Obviously this is not going to go to court but that is the legal position. Take from that what you will.