I suppose it depends on what you are ordering, but some of the best BBQ comes packaged in alumiumum trays if its sliced, or syrofoam containers chopped. Brown or butchers paper is usually used on smaller orders with paper containers, but I think that is to keep costs down. Often, around holiday time, when a whole ham or turkey is smoked and sliced it is packed in an alumimum pan and covered with foil. It's practical.
Burgoo also comes in syrofoam containers unless you buy gallons, then it is in plastic widemouth jugs. I believe part of the packaging depends on where you buy it. All the smaller pits use paper and syrofoam, but I think that's because its less expensive.
That said, the meat is not cooked in, on, or with alumuinum foil.
Regards,
Malta
p.s. Thanks for the probe thermometer information.