Nearly every commercial bottle conditioned beer is filtered or centrifuged and has yeast added back, including the Belgians.
I believe that Belgian beers have more sediment because you are buying them at a year old vs 4 weeks maybe for a Sierra Nevada.
Most Belgians (aside from sours) aren't nearly that old when sold. They simply can't afford to warehouse beer for long periods of time or tie up the fermenters.
Rochefort, for instance, does 7 days in primary (68-73F), 3 days in a cold secondary (48F), and then is bottled and spends 10 days at 73F before being sent out the door for sale. That's
3 weeks from grain to glass if you get it fresh off the truck; obviously shipping time to America and store shelf time add to that.
Most of the other Trappist beers (including Chimay, Westmalle, and Achel) are on fairly similar schedules, maybe up to a week or so longer.
The 2 longest turnarounds for Trappists are Orval and Westvleteren, which are both about 2 months or a hair more.
Orval takes a bit longer (after 4 days in primary and 3 weeks in secondary) because they bottle condition at 58F, which takes 5 weeks or so. That's probably done in part because they use Brett in the bottle.
Westvleteren takes longer because they lager it--it's like 5 days primary, 3 weeks secondary, 4 weeks lagering, and then 10 days in the bottle before being sold.