As much as I am strongly against people accumulating liabilities when they believe within them that they are rich and have arrived, if you are actually wealthy and without debts as you claim, you should be able to afford a car and a house for yourself. No buying any of these does not take away liabilities from you. You will still spend money on renting cars or other means of transportation. Not owning a house does not make you better either, you are still indebted to your landlord.
A combination of both financial discipline and a little comfort and fun is highly adviceable. What is the whole effort for if you can't make life comfortable for yourself?
You are right that even if someone does not buy a car or a house, he will still rent it, and not live on the street or ride a bicycle.
But it seems to me that the author of the topic meant that some people specifically make purchases such as a house or a car to show other people, for example, their friends, how wealthy and cool they are. And this is their main goal, and not the purchase of a car as a means of transportation or a house as a means of housing.