I wrote this article. I think it's more accurate to say "Building software on top of someone else's web api can be a really, really bad idea" -- if you don't do due diligence. I've written about the perils of building on top of consumer web platforms in the past, and personally think there's far more risk in building apps for, say, Facebook and Twitter, than incorporating into your own product a commercial API that you've vetted reasonably well.
Developers/entrepreneurs need to be pragmatic. New ventures that spend all their time and money trying to eliminate risk usually fail; the ones that succeed instead try to manage it. When working to get something to market to see if it will fly, it can be a huge mistake to invest in building low-level functionality from scratch. Most developers/entrepreneurs, for instance, aren't going to build their own video encoding engine. Sure you could use ffmpeg, but out of the box ffmpeg is hardly Zencoder. The time, cost and functionality advantages of Zencoder certainly outweigh whatever risk there is that Zencoder would go out of business in the near term.
In short, it's about cost and time-to-market. Reinventing the wheel usually increases both. So unless you have unlimited resources and already have a strong presence in a market, it's far better to bring a lot of this stuff in-house after you've validated that there's a market for your product and it's making some money.