If, indeed, the park was rented out for a private affair and the person managing that affair asked that someone be removed from the property, then like any case of trespass, it is within the purview of the police to remove that person.
It doesn't make the US look good, but I don't think it reflects poorly on the behavior of the Belgian police.
It probably matters if the park, or the rented sub-venue is a public place or not.
Local laws also matter.
In the US, getting someone removed from a public event without or with fabricated cause is likely to cause problems down the road, as the removed people might be likely to win lawsuits.
Belgium has probably - like the rest of the EUb - far weaker freedom of speech protections,
But IANAL, and just a second rate, third hand armchair commentator.
Could be but I am not sure belgian law is as trigger-happy with the whole trespassing thing. I wouldn't be surprised that lying to the police about someone being a threat in order to remove them form the private event you have invited them to would be a clear cut case
I suspect if the Greek embassy had rented a park for an event, and then told diplomatic police that there was someone there they considered an active threat, much the same thing would have happened.
People have forgotten because it feels like eons ago but at the beginning of Trump's first term the Turkish president on a diplomatic visit to the white house sent his goons to beat peaceful American protestors while the American police did nothing to protect Americans.
If, indeed, the park was rented out for a private affair and the person managing that affair asked that someone be removed from the property, then like any case of trespass, it is within the purview of the police to remove that person.
It doesn't make the US look good, but I don't think it reflects poorly on the behavior of the Belgian police.