In this instance the innuendo is clear - this man is suggesting that your lips (mouth) or more likely your genital lips will be inflamed by sexual activity.
It's anything but clear - there's pages of people with different views on it here alone. I can certainly see both sides, but even with the low threshold of probability required in employee disciplinary cases, you're talking about taking a serious action (written/final warning or worse) based on something that could quite plausibly be a misunderstanding.
We also have zero surrounding context (outside of a OP referring to the man as a creep), so to say that it is clear, simply isn't correct.
As a general rule, raising a formal grievance about things like this will definitely change the culture, because organisations are very wary of having a paper trail like this.
She has raised a formal grievance and it's been rejected. So if what you say is correct, then OPs claim must have had very little merit, or there are important details/context missing.
It could be that they've interviewed everyone present and found them all to agree that it was clearly a misunderstanding on OPs part. It could be that their HR are shit. It could be anything, we don't know.
I agree with you that these processes play an important part in changing workplace culture, but they also shouldn't be deployed willy-nilly and they certainly weaponised against people you think are a bit weird, which is another potential scenario here.