I know they wouldn't have have the brands as prominently placed as they do now, but surely brand or store names would have appeared on labels inside clothes?
Obviously this is a joke within the movie, but would it be so rare that this mistake could be made if one was to travel back in time?
What was new and novel in the 1980s was full personal names of individual designers on mens clothing. Prior to that, brand names for underwear had primarily been corporate names such as Jockey, Hanes, BVD, Fruit of the Loom, Fieldcrest, Pilgrim (Sears), Signature (Montgomery Ward), etc. Even for mens suits, ready-to-wear names were things like Hart Schaffner & Marx, Botany 500, Brooks Brothers, Bond, individual department stores, or names chosen to evoke tweedy associations with London tailoring. Only in the late 1970s did individual designers—Pierre Cardin, Alexander Julian, Bill Blass, Ralph Lauren—become menswear brands known to the average consumer.