Please read the comments for that quest of WoWHead - this has been known about for a very long time it seems.
"By Toxoid (312 – 1·9) on 2011/01/31 (Patch 4.0.3) Report
For the skinners, I don't know if it's a bug or something but after you've mutilated the basilisks, you can still skin them, you won't get leather from it, but still get the skill-ups.
BUT: If you skin them, the corpse doesn't disappear and if you wait some time (like 1 minute or something like that), you can skin them again, you can easily level your skinning this way, but you won't get any leather from it
I guess this will be fixed soon."
The only difference is - you skinned 5 of them - which may or may not of taken you a minute.