A lawyer might argue that, but it's not going to be a compelling argument. Recklessness is generally a conscious disregard of the consequences; as applied to defamation-like claims, it's generally seen as "you specifically voiced doubts about the truth". Failing to vet automated abuse reports is going to be at best negligence (and I'm dubious of even that, because given the nonbinding nature of abuse reports, it's not clear there is even a duty to candor in abuse reports that one can be negligent of), absent internal complaints about "the accuracy of these things is total shit".
Knowing that you'll absolutely generate false positives and not providing a method of automatically fixing those would be a deliberate action, not recklessness or negligence. I wouldn't be surprised to find code that pings staff based on account size.
It seems like providers could remove themselves from the situation by just giving their clients a "fair use!" response button?