Turns out it is Briggs who claims the kiss was on the cheek, the woman says it was on the neck. A significant difference imo.
Not really. As a famous missed kiss of Prince Charles to then Princess Diana showed, she moved so it missed his mark. He ended up awkwardly kissing her neck where he'd aimed for her cheek. Further, Briggs might have been aiming for the mouth for all we know. The point is, the move was entirely inappropriate and unwanted. There must have been more about this behaviour contextually that give rise to the complaint than just a simple kiss on the cheek by way of greeting or farewell.
Also read she reported the incident the next day to an interdepartmental authority as she felt Briggs needed to be made aware his behavior was inappropriate though had no desire to see it go any further than that.
Whatever her personal desires were about limiting the matter, there is a public interest in standards being met and being enforced.
She might have been worried about retaliation. This is possibly the biggest problem with sexual harassment. The experience is bad enough, but the perpetrator who experienced a slight (of their advances being rejected) can badly damage the victim's career in hurt pride retaliation. If the woman wants to take the matter further, it can damage her career as well, sometimes permanently. That's a no-win situation and it's the reason why a lot of sexual harassment goes unreported and it is far more prevalent than it should be.
Fortunately, Turnbull obviously senses that he cannot brazen this out and needs to set some standards. He was squirming uncomfortably in his seat on the day that Gillard delivered her misogyny speech as he well knew that the antics of Abbott and mates had gone on unchecked for far too long. Turnbull might have some limitations, but he has standards in his personal dealings. Kudos to him for at least that much.