The answer in most cases is "yes".
This post is full of the kinds of flawed arguments that usually accompany pro-rent arguments -- which do a real disservice in identifying those cases where the answer is "No".
Breaking down the problems by section:
Equity
"Here’s the rub: Only a small slice of your mortgage payment builds equity."
There you go, the article defeats itself not even a full screen below the correct answer.
If you rent, 0% of your monthly payments build equity.
If you own, X% of your monthly payments build equity.
X > 0
It attempts to list all the parts of a mortgage payment as if itemizing it makes the equity earned meaningless.
Your mortgage consists of four parts:
Principal (the equity-building piece)
Interest
Taxes
Insurance
This is basically correct, but the case for "Your rent consists of the same four parts + two additional parts where the property owner may make a profit off of you as well as some additional money to cover various expenses that they'd rather not pay for out of pocket."
Again, nothing in this section invalidates that building equity is better than not.
One way of thinking about renting is that you pay all of this, plus the extra stuff and in the end you've built equity for somebody else and none for you.
Opportunity cost
I didn't bother to read this to be honest, these sections are almost entirely filled with notions that "if I just invested my money in horse farms or leverage backed security instruments I'd make more money in the long run" blah blah blah. The logical flaw in these are usually pretty easy to spot as they involve a scenario setup that's not like-for-like (meaning the same house as a renter vs. as a buyer) and focus on weird time frames like the lifetime of the loan not the life of the person.
In other words, at the end of 30 years, the rent may have made more money in some scenario of a perfect investor, but then they still have to rent to have a place to live. The homeowner now owns their property free and clear and can do all kinds of things with it, and their now future income is entirely liquid.
Should I rent of buy
Do what you want! But don't follow the flawed arguments in this blog. Here's what it really comes down to, do you want your money to be more liquid and your location to be more mobile? Then rent.
Do you want to own large amounts of assets that can be liquidated in a few months (in most places) or that you can live in virtually free in the future? Then buy.
Bonus: if you buy, you can end up in a situation where you just have other people literally giving you money to pay your mortgage away...it's called being a landlord. You can even do it with parts of your property, like a bedroom or a basement. Over time you can own a property outright, rent it out, and use that rent to service another mortgage in a property where you live meaning you live virtually free and accrue assets at a frightening rate.
edit once again, here's probably the best post written on the subject.
http://assayviaessay.blogspot.com/2014/04/rent-or-buy.html