"that they're still fermenting actively when served"

That was true of beer brewed hundreds of years ago so it would have some carbonation and its sourness would be tolerable but it is not true of any modern brewery. Unless they want exploding cans.

Even though hazies are best drank fresh they go through all the normal fermentation as any other ale. Otherwise they would be rough, estery, butter bombs from not giving the yeast time to clean themselves up. Many breweries just screw them up as it's one of the harder styles of beers to do properly.

If the hazy your drinking has yeast sediment in the bottom of the glass/can it was done wrong.