If refs hadn't been blatantly going out of their way to help them to absurd degrees, it might be possible to find it in oneself to believe that they really hadn't been buying favorable treatment. Anyone who has kept even half an eye on La Liga throughout this period knows that refs have practically been fellating Barcelona in the pitch, though.
If we disregard that fact, it's still incredibly suspicious and indefensible to pay millions (and go to great lengths to hide that fact) to the head of the ref's association. And if we don't disregard that fact, it's impossible to believe that they did in fact pay for innocuous "reports" that weren't in any way unethical or underhanded. Simply impossible.
Whatever the case, since we know for a fact that these payments took place, that alone is bad enough that if Barcelona go unpunished, the credibility of La Liga is completely gone. What's to stop any other club from sending wads of cash to referees? Short of those refs personally admitting that they've been repaying that with favorable calls, which they would never have any reason to do, how could anyone ever prove that such an exchange occurred? It would be a free license to cheat.
This is why officials in most industries and environments that have any pretense of fairness aren't allowed to accept gifts from those they're tasked with arbitrating. You can't just send a million euros to a judge presiding over your lawsuit and say that it was just a gesture of goodwill, no harm intended. If that were allowed, everyone would do it, and how could anyone then determine if it had an influence on the outcome unless the recipient just confesses it for no reason?
Realistically, all it would take for Barcelona to get away with this, if they have in fact been buying ref favors but the lack of concrete evidence of this fact meant they're acquitted, is for the refs who have been doing it to simply... say they hadn't. And for what possible reason would a ref admit they had done this? It's not as if these guys will have been stupid enough to arrange it via e-mails that they printed out and stuck in a filing cabinet. If it took place, it'll have been through untraceable channels, like verbal agreements.
That's why you can't pay under-the-table money to the guy in charge of the fecking ref's association. Anyone who can't see this has probably never worked in any field where ethics concerns are a factor. This is the most basic principle of professional ethics. Even if they never prove that it influenced refs, the payments themselves are profoundly incriminating, and if La Liga has any pride in itself, it justifies a severe punishment. In what world should a club be allowed to do this? It'd be absolutely insane.
If there was any legitimate, above-board reason to pay millions to the head of the refs, Barcelona would not have gone to such great lengths to hide the fact that they did. It's as simple as that, and that's enough to make them deserving of a heavy punishment. I'd say that if it can't be proven that they were actually paying for favorable treatment, a large points deduction is still in order, as well as a truly huge fine. If it can be proven, however, relegation (preferably by more than a single tier) is required, and possibly revoking titles.
Ask the owner of a company what'll happen if they try to secretly bribe the tax auditors. This is the same thing.