IANAL but my understanding is that the FCC cannot arbitrarily change policy; there is a specific process and they have to do certain things (or more precisely, they have to be able to argue in court that they followed the process). The relevant law is the Administrative Procedures Act, which among other things requires a public comment period for changes in policies and rules (and requires that public comments be considered before the final rules are established). The purpose is to avoid the situation we are in now, where regulations change whenever political parties change, which, ironically, is one of the reasons some ISPs opposed this latest change (ISPs need to make long-term plans, which is hard if the rules might change every 4 years).

So my understanding is that the law was broken because the FCC's rules change was arbitrary, rather than motivated by facts, and because they ignored expert commentary (including from the people who created the technologies discussed in the FCC's analysis). The final rules did cite various comments, from both ISPs and independent experts (myself included), but the pattern was pretty obvious: anything that does not support the FCC's case is dismissed as "not persuasive" while supportive comments from ISPs are cited as proof that the change is necessary.

It was all for show; from the beginning the FCC basically said that they were not at all interested in comments about technical facts, only about their legal authority based on the technical analysis they presented in their proposed rule change (i.e. they can make any claims about facts to justify a change in the regulations). The commissioners already made up their minds before opening the comment period and never intended to have comments affect their decisions. Whether or not that is allowed by the law is now a matter for the courts to decide.

Administrative law has all kinds of requirements regarding process and motivation. For the most part, the arguments in the legal brief (https://blog.mozilla.org/wp-content/uploads/2018/11/as-filed...) are about decisions being "arbitrary" e.g. not properly justified by public interest.

This is part of why the Obama era's regulatory changes in e.g. telecoms and finance reform took so long to get through the system - they dotted all the i's and crossed all the t's. This is a much more durable way of changing things than an executive order, since it can't be overturned on the whim of the next president.

It is also worth pointing out that Tom Wheeler's decision making was impacted by public comment -- his proposal went from weakening net neutrality rules to a fundamental shift in how ISPs are regulated after a public outcry. Ajit Pai was never going to be affected by public comment and completely dismissed the comments people submitted.

Federal agencies are not absolute monarchs in their domains. They can issue regulations only that comply with their mandates from law and that were produced according to procedures as stated in law. In this case, they have to go through a fact finding procedure, get public comment, and show evidence for their decisions.