I located the problem and fixed it using baksmali/smali. I then opened a ticket on their public Jira server describing the problem, solution, and even attached the patched .apk. Months later they still haven't merged it into Skype proper, even though it's literally a two-line fix. In the meantime loads of people cannot use Skype on their phones.
The fact that a company that is supposed to be worth 1 trillion USD doesn't have the manpower or interest to fix such a simple bug that totally breaks their product for a lot of people should tell us something. From the outside it looks like all the skilled people have left a long time ago, and I wonder if they'll be able to maintain their market position like this.