There's nothing wrong with depending on 3rd party tools and products. The problem is that most of the REST APIs that people are more and more dependent on are services, not traditional libraries.
If a library vendor goes out of business, I still have the last copy of the library and possibly even the source code. My product can continue to function until I find a suitable replacement. This is an acceptable cost of doing business, especially since commonly used libraries rarely just disappear.
If a service API goes down, my product is essentially bricked until I find and implement a replacement. This is one of those risks that most modern (er, young) developers don't appreciate. We haven't had a bust yet that shuts down a number of services over a relatively short period of time (hint: if you're using the service for free/at-a-cost-less-than-power-consumption or if it's not the vendor's core business, such as Parse, there's a good chance it will go away at some point). When that happens, the successful apps that relied on less successful services will be in a tough spot.
It'd be fun to do an analysis of the various API services people use and their interdependencies. I bet we'd find a few really scary single points of failure...