Yes it does shield you fron rent increases. Specifically because by owning a home you have also purchased an income producing asset that perfectly hedges your rent increase. For every dollar that rent goes up and you have to pay more, you also get an additional dollar in income from that increased rent. Ie shielding you from the affect of any increase.
It's the same thing as buying a stock, and then shorting that same stock (or buying a put). Yes the stock may go down, but for every bit it does, your other investment up down meaning you are now shielded from (or hedged against) any changes in stock price.
Inflation is the best thing that can happen to you if you owe highly leveraged debt on appreciating assets. The more debt the better.
Your debt payments stay stable, the asset price goes up, your wages go up, and within a few years the payments are negligible compared to your salary.
Compare this to a renter - your rental payments go up, your wages go up.