My theory is that, as usual, they need vehicles to rob from the club. Other common practice are commissions when a player is bought. But this is limited to some players, not so easy to maintain in time, etc.
You need to know that the counterpart is ok with corruption and you need to trust that person.
They probably thought that Negreira was a good fit to get some extra greens. They knew him, he was from Barcelona, he could sell legit stuff (ethical != legal) like the referees reports on a recurrent basis. His son had a company offering football services (and worked for other Spanish teams/institutions)... They pay him a lot more than those reports (typical political corruption) cost and they split the money. Not a lot of money for Barca but it can help some individuals. Then you are in a spiral that is difficult to leave.
They probably didn't even think about him in the sense of "vice president of the referees" (again, not exactly that but I won't counter that). The whole business was legal, wasn't hidden. It was reported and it paid taxes. I would imagine that if you really want to buy the referees, the only thing you will never do is leaving any trace of payments to anything related to the referees. If that isn't your intention, then you can probably be focused in how to "sell" those services legally.
Bartomeu for example did that to insult some players of the team on social networks (imagine...), so nothing new to consider. It has been an ongoing issue with Barca. Not a single referee has told a thing (and there should be dozens of retired and harmed referees who should knew this if this was a real thing). Payments were public and legal. Specially those things don't click when you imagine a bribing referee scheme.
It also explains why Barca presidents and executives are not as clear as you would expect. Because they don't want to explain that Barca wasn't bribing referees telling that the real deal was that they were robbing the club. On one hand they need to defend Barca, and on the other side they need to deflect their guilt. Money only proves corruption, but the prosecutor needs something else to prove referee bribing. If my theory is true, no bribing prove will be found and Barca will be declared innocent (or not guilty) from those charges and they would only need to deny everything and hope that no trace of inflow money is found to them.
My theory is not based in senseless love for Barca, but in the behavior of the executives in the last decades.
Another interesting stat that you won't find in a ultramadridista blog is that Barca has scored more goals in LaLiga than Real Madrid since its conception. That Barca has received less goals than Real Madrid in the history of LaLiga.
However, Real Madrid has been granted way more penalties than Barca, that Barca has suffered way more penalties than Real, than Barca has had more red cards than Real Madrid and that Barca rivals have received less red cards than Real Madrid rivals.
It means than Real Madrid scores a way bigger percentage of its goals form the penalty kick, and that Barca has historically received a way higher % of goals from the penalty kick. All that after supposed 20 years of robberies and scandals... interesting huh??
That is actually my biggest "mmmh..."
However, at that point Barca financial situation was starting (or more than that) to be, at least, worrying. Depending on that, Bartomeu himself could have some liabilities, so even if you got a slice, it doesn't seem a bad idea to stop it.
Bartomeu said that they just stopped doing that to save money and that they started to do it internally. It can be true of false (as 90% of the things he says), but that is purely circumstantial.
By the way, my last message of the day. I will probably be back tomorrow