I had a very similar experience
A few months ago I received an email from Paypal saying my account had been debitted, then another, then another, all with reference to my Skype account.
I immediately tried to login to Skype but got an invalid password message, so I emailed both Skype and Paypal. Paypal responded pretty quickly with a dismissive email, and Skype ignored me.
Since my account was still open for abuse by the scammer, I figured the only option for me was to cancel the account in Paypal and call my bank, who immediately cancelled the credit card.
After about 4 days, Skype finally responded to one of my pleading emails, saying they had reset the password for me but that any fraud was nothing to do with them. I logged in to find my call history consisted of calling a premium number abroad.
About 3 months after the event, my bank contacted me to say Skype had agreed that the transactions had been fradulent after all, and my money would be refunded.
Avoid Skype like the plague, they're the worst company I've ever dealt with for customer service.
Most premium number scams would be pretty simple for Skype to block, simple don't allow any calls to a set of blacklisted numbers, and look for unusual calling patterns to new numbers generating large charges, but they're obviously not interested in helping their customers.