There's a distinction between the above statement and the truth, which is that CloudFlare and other large CDNs do not work in Spain when there are football matches.
Yes, it's not CloudFlare's fault in this instance, since I believe CloudFlare is not being notified to take action in real time. The blocking needs to happen quickly to block access to illegal streams of a live event. My understanding is that CloudFlare is largely out of the picture when this decision is happening, and CloudFlare is only taking the blame since that's what Twitch uses, which also can't react as quickly as La Liga wants.
That being said there is a solution to this that helps protect from collateral as well as the decentralized open nature of the internet: moving away from those large CDNs