Battery Discharging during use of Skype On Charger!?

Unusual but not unexpected.

This Apple article has a subtle bit of wording that probably explains what you see:

http://support.apple.com/kb/HT2332

specifically this:

If the battery is removed from a MacBook or MacBook Pro, the computer will automatically reduce the processor speed. This prevents the computer from shutting down if it demands more power than the A/C adaptor alone can provide.

(my emphasis)

This seems to say Apple anticipated some very demanding apps would need extra power, requiring the battery to supplement the A/C source.

The fact that your fans spin up supports your observation about the app being a kludge-hog.

Skype video calling is a monstrous energy hog, and when you do it, your MBP is demanding more power than its AC adapter can provide. Under those conditions, the battery is drawn upon to make up the power deficit. This is by design, and is the way the machine is supposed to operate.

To limit the impact of Skype video calling, you can either a) not do it, which is what I recommend, or b) make sure nothing else is drawing power at the same time: no bus-powered peripheral devices connected (hard drives, iPhones, iPods, iPads, mice, trackpads, joysticks, etc), no other apps running, and no power-hungry background processes eating up processor cycles.

You may want to try resetting the SMC:

http://support.apple.com/kb/HT3964

Doing so can sometimes sort out power-related anomalies.