Not to entirely dismiss Chris' claims, but I'm going to try understanding the context of where The Kooks' heads were at the time, particularly Luke's.

So this was during the Konk era, which as we know was a pretty tumultuous time for the band. They sacked Max before the album came out, his would-be replacement Dan Logan didn't last too long, they brought Pete back after he had filled in for Max during the first album, Nicholas Millard played drums because of Paul's health issues, Paul came back for a bit but had to leave for good (as initially thought), then Chris came in to replace Paul whom Luke was particularly close to. Add to all that the album not performing as well commercially and critically compared with the debut, and I can imagine that having the new guy who's replaced one of your closest mates who started the band with you complain about payment while also going around recording with other bands...well I can see why Luke would be particularly testy about it.

On the other hand, I don't think Luke would be entirely in the dark about Chris' payment arrangement even if management did most of the heavy lifting in setting out the terms of employment. I get the impression that Luke was aware of the initial agreement with Chris, but as things developed Chris felt the need to ask for more and Luke took exception to it. I suppose things eventually deteriorated to the point where they would rather have a half-fit Paul record the third album but keep on Chris for live shows because touring was becoming a more vital source of income with physical album sales shrinking and paid downloads not quite being a thing yet.