The HHR is based on Chevrolet's early panel vans (and/or Sedan Delivery) which predated Plymouth's earliest unsuccesful attempt at the market: 1930. Plymouth brought their panel/delivery back in the mid-30's and it ran for about 7 years.
Chevrolet (and Ford) had a panel/delivery option in the 1920's and the option remained available for over 50 years.
So I don't think either is copying the competition, they are simply touching back on their automotive roots.
Technically, though, Plymouth was a late-comer to the game.