First of all, the headline is ridiculous. A person is not "homeless" because he chooses not to own very much. That trivializes the situation of the truly homeless.
But to get to the substance--yes, it can be Mustachian to choose to rent many of your possessions. It can be hard for homeowners who have lived in the same large house for decades to understand this, but owning stuff has costs, not just in the initial money cost, but the cost, but in having to find space for it, care for it, move with it and, if you move, find new housing big enough to store all your stuff.
This is why I have a gym membership--common Mustachian advice is that I should just buy thousands of dollars worth of stuff, store it in my garage, and then, presumably, find some way to sell or transport hundreds of pounds of weights when I move. That sounds like a whole hell of a lot of work and expense when I can rent an entire large gym's worth of equipment for $40/month. It's a lot better than what any home gym has; I never have to clean it or maintain it; and it'll still be there if I move. Apartment dwellers also don't have the option of buying a washer/dryer, and a lack of free parking makes car ownership more expensive.
So yeah--consider your life situation, and renting anything may well be better than buying.