The reality is that if you rent you may not show as much debt but there is still an implied debt obligation because you need to live somewhere
I don't agree with this at all for the same reason that you don't include implied debt obligation for people that take the bus versus having their own car.
Couple of differences in your view though:
-housing whether rented or owned tends to be largest monthly obligation that people/households have.
-when buying a house most (not all) are deciding that based on some payment that they are either comfortable with or approved for, not much different than renting.
-taking the bus is shared transportation service normally subsidized by the government, so if you are saying that the choice is between (a) buying a small fraction of a car with a loan or (b) taking the bus then I would agree.
My point was that regardless whether you rent or buy there is usually a monthly payment....rent you have payment with no debt obligation.....buy you have a payment with a debt obligation that is backed by an asset.....the inverse of the implied debt is to ignore the mortgage debt to the extent the value of the house (adjusted for transaction costs) exceeds the debt.
All that aside, the point is that people live somewhere and there is a cost, the fact that millenials are forming households and buying houses at a lower rate or at ages older than prior generations (whether by choice or inability) means that they will inherently have less debt because mortgages are typically the largest debt that people incur.
Edit to add: The trend of millenials not buying houses or cars is starting to shift as rents continue to rise, employment options increases along with the economy, and they begin to cohabitate and have children. If this continues then I would expect the millennial debt loads to increase. Compared to the prior generation millenials are about 5 years on average behind in this sense but it seems to be getting there.