I went to Japan with some friends for 3 weeks, and we just couldn't figure out how these stores are stocked, we didn't see any familymart, 7 eleven or lawson trucks. At some point we just kinda assumed everything was stored frozen in the back, but the article's line: "Lunch is a busy time at the konbini. Konbinis have large scale operations that deliver fresh bentos (lunch boxes) to stores" refutes that assumption.
I guess maybe the trucks they use just aren't branded? Maybe we just were never in the right place at the right time?