If there is a fine line between law and order and chaos, there is an even finer line between what the police can and cannot do.

And if we have learnt anything from the fallout from Saturday’s police-sanctioned neo-Nazi rally outside NSW parliament, it is the size of the chasm between those who make laws and those who enforce them.

Into that gulf have fallen questions about how the police can act and when, what protections can be offered by the laws touted to keep members of the public safe from vile vilification, and how unsafe the community must feel before authorities are able to intervene.

As time stretches on and those unanswered questions pile up, Premier Chris Minns and Police Commissioner Mal Lanyon have found themselves at the centre of a public relations nightmare just weeks into the latter’s appointment.

For days, two of the most powerful men in the state have refused to point the finger at each other over whether lax laws or inadequate enforcement was to blame, bearing equally the brunt of a debacle that has left both red-faced and scrambling for answers.

Lanyon, along with other senior police, remains steadfast in his view that police were powerless to stop the protest from going ahead. What the 60-odd members of the National Socialist Network did – call to “abolish the Jewish lobby” and protest against hate speech laws targeting groups like theirs – was not illegal.

While legal experts say police already had necessary powers at their disposal to intervene, Lanyon maintains the legal advice officers in the CBD’s local area command received was clear: the banner the NSN proposed to display at the protest did not constitute an offence under hate speech laws. Had the word “lobby” not featured on that banner, it may have.

That the NSN’s protest fell on the right side of the law is no stroke of good fortune. To the frustration of police and politicians, the group has become adept at navigating the grey area of the law.

Leaders of the NSN have spoken openly of the tens of thousands of dollars raised to fund legal advice and hire lawyers to keep, or get, members out of trouble. Such resourcefulness presents law enforcement and legislators with an uncomfortable reality that makes policing the group all the more challenging: they are acutely aware of how far they can push the boundaries and remain clear of a set of cuffs.

While agencies including NSW Police and the Australian Security Intelligence Organisation (ASIO) are monitoring the NSN more closely than ever, this week has made it alarmingly apparent that taking action against the group may be more difficult than previously thought.

It is terrifying to consider that authorities may not have the powers to stop a group whose “hateful, divisive rhetoric and increasingly violent propaganda” ASIO director-general Mike Burgess last week said could inspire “spontaneous violence”.

Much has been made of the communication disaster that left Lanyon in the dark about the protest. Both he and Minns only knew the rally took place on Saturday because the Herald sent questions to Minns’ office.

Lanyon’s force has been rightfully criticised for a bungle that has been worsened by a series of revelations about who knew what about the protest and when.

That one of his deputy commissioners, Peter Thurtell, was briefed on the protest five days before it was held and did not relay the information to Lanyon is deeply embarrassing for both Thurtell, an experienced and extremely well-regarded officer in the twilight of his career, and his boss.

That another of Lanyon’s deputies, David Hudson, who oversees counter-terrorism operations and has been NSW Police’s public face of antisemitism, was not aware of the protest despite officers in his command providing a briefing for local police who attended the rally, is a long way past concerning.

In an organisation as large as NSW Police, which has more than 20,000 employees, information can fall through the cracks. But for the commissioner and the force’s most senior counter-terrorism officer to be out of the loop on the activities of the group that was put on the national agenda by the country’s spy boss days earlier warrants a thorough explanation.

Thurtell fell on his sword on Monday night and admitted he had been aware of the rally but had not relayed the information to Lanyon. He said he had apologised to Lanyon for the “oversight” and the pair had made good.

Thurtell’s explanation for the gaffe – the information he received suggested no laws were being broken. Had it, he would have fed it up the chain.

While the lack of communication at the top of NSW Police in the past fortnight has been rightfully scrutinised, most concerning are the holes the saga has revealed in the government’s much-vaunted race hate laws and in authorities’ ability to control the NSN’s growth.

Minns has vowed to strengthen laws to put more powers in the pockets of police. “It’s likely the case that we need to give police more legislated powers to stop this kind of naked racism and hatred on Sydney streets,” he said after the rally.

But he now faces the challenge of drawing the line between hate speech and free speech in a way that will not be seen to be stripping people’s rights to peacefully gather. At a time when protest groups are tallying up the wins they have over NSW Police in the courtroom, he will need a fine-point pen to craft strengthened legislation that will garner enough support to make it through parliament and onto the streets, and score points with police and public.

But without change, Saturday’s rally could become a regular fixture on the NSN’s calendar while police are forced to stand idly by, handcuffed by the rules they swear an oath to enforce.

Start the day with a summary of the day’s most important and interesting stories, analysis and insights. Sign up for our Morning Edition newsletter.