Yes, there are differences... a lot. It's not just a myth, but that is not always a bad thing.
There are some features which are just plain missing from WP. One example is the ability to determine which carrier the device is connected to. That was something WP8.0 apps could "kind of" do, but WP8.1 (windows runtime) apps no longer can.
Overall though, for the most part, iOS and WP are quite comparable. Android however is a completely different beast. It's probably simpler to ask what Android apps can't do. The thing is, these differences are not so much oversights on MS' behalf, but rather deliberate and conscious decisions MS has made in the interest of stability, reliability, performance, battery life, security and privacy. For example, some developers may find it annoying that their apps can't access your text messages, but from MS' point of view that is a sacrifice worth making in the interest of privacy and security. Considering text messages are often used to regain access to websites (after forgetting our passwords), or for two-factor authentication, I would agree, but it's not completely crazy to be of the opposite opinion. Similar restrictions exist all throughout both iOS and WP, many of which provide profound and important benefits, where Android has none or very few. Which you prefer ultimately depends on what you are looking for in a smartphone, and how highly you value those traits I listed above over flexibility and features.
Finally, developers will sometimes blame difficulties on API restrictions, where blaming the developer would probably have been more appropriate. Blaming API restrictions is easy to get away with in the WP community, because it's just reinforcing a preconceived (but not entirely untrue) notion. If you're not a developer, you just don't have much hope of validating which claims are justified and which aren't.