It's quite true that the quoted statement:
“Securus requires documentation and reasonably relies on the professionalism and integrity of our law enforcement customers and their counsel. Securus is neither a judge nor a district attorney, and the responsibility of ensuring the legal adequacy of supporting documentation lies with our law enforcement customers and their counsel.”
sounds pretty strange.
As a company that has access to confidential data, they are responsible for the privacy of everyone using the mobile telephone system. So one would think they would be responsible if they released this data without taking adequate precautions against improper release.
However, the law as it stands in the U.S. may not place an absolute onus on them, and voluntary cooperation with the police, without requiring a court order, is certainly not criminalized for data that a firm holds itself.
Functioning as a back door to data about users of other telephone providers, though, is an invitation to abuse, especially when a firm is known for being less questioning of requests from law enforcement sources than others.
Hopefully, the firm at least keeps careful records of every such request that it receives, so that any improper requests can be tracked by the relevant authorities? That would seem to be a minimal step to take in order to ensure that the responsibility does lie with the requestor and not them.
But even if no one at Securus is jailed for violating privacy, a possible consequence, if they're not complying with standards expected by other telephone carriers for the handling of the data to which they have access as a telephone carrier themselves... could be being unplugged from the telephone network, and thus losing their business. I mean, I presume they had to sign something to become a telephone carrier.