I found a photo on flickr of some Mangalitsa pigs.
When she's in heat, he'll follow her wherever she goes. So they are breeding in the muck because that's where she chose to stand. As the photo shows, there is drier land nearby - but that's not where she wants to be. She likes to be bred in her own manure.
Here's pigs on a farm in Austria. They are in muck too - it really smelled like hog manure.
But it doesn't seem to bother them - pigs being pigs, if they weren't happy in the pen, they'd bust out. They'd rather be in the pen with the food, even if they are always smelling their own manure.
In the end, what matters is how pigs taste. Mangalitsa pigs, fed the right stuff, can be raised in muck and still have meat and fat that tastes incredible. They can be raised in clean stalls and taste incredible too.
It doesn't matter if one raises a Mangalitsa pig in a filthier pen, in a cleaner pasture, in a confinement barn, etc. -- so long as you hold the diet and age at slaughter constant, the Mangalitsa will taste more juicy and flavorful than other breeds of pigs.