AGPLv3 solves exactly this problem.
The question of open source is really -- do you have a secure upgrade path. If Windows goes away, and software you use depends on their software, you do not. If you use software based on a BSD/Apache2 license, and someone extends it and makes the result non-open source, and the software you use begins to require these extensions, you don't have a secure upgrade path anymore. GPL solves this problem and guarantees that you will always have an upgrade path, because derivatives need to be open source.
I think this is really the key point, and why purism in software licensing should not be laughed at by "pragmatists". Like for example distributions that do not include closed source software (Flash) or drivers (nvidia), because "pragmatists" want it to "just work". If you go down that path, you are making yourself dependent on a company going the path you want. You get into a situation 5 years down the line where even more software depends on closed source (e.g. mono/.NET), and it is out of your control. That's why I think purism in open source software is still relevant.
Pragmatically speaking, the upgrade path of open source software packages is not in your hands, but in those who are experts in that package's code, and those who invest time in it. The point is rather that if you get annoyed enough to pay someone, you would be able to get control back, while with closed-source extended BSD/Apache2 packages, you would not. You would need to re-invent that software.
For Web services, I think it depends. If the company provides proprietary data, then it doesn't really matter whether the software to access it, or the API is open source. You will have that dependency, until you have open data.
In summary, I think one should ask oneself: In 5 years, when this platform is outdated, and the company goes away or refocuses, what will I do, and am I prepared for that. Who am I dependent on? Having a community of millions of programmers which are in the same situation helps, because only one has to solve the problem and open-source it for an upgrade path.