Colin reported the same issue today to me.. I tested here with a secondary account that I have with teh same access as you. I was able to download it just fine.
Please be sure to go to teh website main page, and hold down SHIFT while you hit the reload button in your browser. Let me know if it works after that. I am seeing people with cached copies of the page and the link is still wrong.
Thanks for posting about this Guys, I discovered that I had made a major mistake when configuring security on that module and basically everyone in the group was Denied DOWNLOAD Rights, so that is why you would have got Access Denied.
I removed everything and started over today, configured it all correctly and re-did the Quick Document Links.. Please test this and let me know if you have any further problems.