I think the important part might be the top-watering, and not the type of container you're watering into. The common ground with both undrained tubs and circulating bogs is that there's frequent water flow from the top to bottom. Do you have any drainage holes in your tubs? From what I've been told, it's generally a good idea to put a few drainage holes somewhere between half and 3/4 of the way up the side of the tub to let water out if it starts to accumulate and stagnate.
I might be wrong, but I was under the impression that Bugweed's tubs were more to do with concerns of space and water supply than general cultural preference; they worked for him because he had tons of plants that needed to be kept in a compact area, and he had lots of light and evaporation so keeping open trays filled was difficult. What are your temperatures and humidity like? If I recall, Bugweed lives in a warm, semi-coastal area where it's not too humid and there are reliable winds. From what you've said, I would suspect that there's an excess of heat and moisture in your trays, and either some sort of microbial attack is overtaking your rhizomes, or you've got snails or worms or some other chewing invertebrate that are physically injuring the plants and making them susceptible to rot. What media are you using? Is there a top-dressing? How deep are the tubs? Do you have any associated plants in the containers too, or is it 100% Sarracenia?
If this is something that seems to be happening to your whole collection at large, I would wait for a cool(er), rainy/overcast day and dig up a few plants that are either ailing or unaffected but not dead entirely, and look for signs of pest damage. Also keep an eye out for anatomical problems like shallow root systems - I'm not certain what you'd be looking for but if it's a problem with conditions, there will likely be some telltale growth characteristics.