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Sites want me to download newest version of Adobe Flash Player when I already have it

Answers: Have 3 answers
I am having difficulty when at a site that I want to watch a video on (most recently a work site) and I am told I need to update Adobe Flash Player. I double check andI Have the same version I am being insructed to download. I tried going to Security under System Prefences and under Apps allowing from anywhere in case that was the problem. Still, I cannot watch the video. Any ideas of the problem?  I was just watching videos from this same work site without this coming up. I have also had it come up on other sites (less trusted than this site) and could not watch the video because of the same reason. Ihave AdobeFlashPlayer set to automatically update.
The best answer: Assuming Allan's advice is not correct, and you do run the installer, I think I've heard of that problem and it involves removing the old Flash plug-ins, then install the new version. I don't use it so I don't know what they are called, but will be the /Library/Internet Plug-ins folder.
You can go here and enable HTML5 in YouTube so you don't have to use Flash: http://www.youtube.com/html5
Most(?) of the content is HTML5, but you may run into videos where you still need Flash.