The ambiguity here really hinges on how you interpret the phrase "receives healing". Spending Hit Dice during a rest indisputably restores HP, as per PHB p.186: A character can spend one or more Hit Dice at the end of a short rest, up to the character’s maximum number of Hit Dice, ...
This one is because someone sleeps in medium or heavy armor, but you could adjust it to sleeping on hard ground without bedrolls or something similar: When you finish a long rest during which you slept in medium or heavy armor, you regain only one quarter...