That's actually the opposite of "pedantically" given that you're playing loose with the definition. Pedantically, shorting is selling a financial instrument you don't own, with the idea (though it is not a requirement to fit the definition) that you'll give it back later by buying at a price lower than it is now.

What you described is options trading, one method of which hedges against declines in stock price. Yeah, one could take a "short" position by buying puts, but it can be argued that a short position is not what puts were originally designed for. In contrast to short sellers who obviously intend for the price to go down, or they won't make any money.

I do question whether puts are the "more common way" given that they have an expiration. You can hold on to a short sell as long as you can pay the interest and the loaning party doesn't want their shares back.