I just loaded "9to5mac.com" and let it sit for a little while.
I received no "flash player update" message.
Do you actually have Flash installed?
(I do)
If you have it installed, do this:
Open system preferences -- Flash Player
Go to the updates pane
Click "check now"
What result do you get?
Something else I would recommend (just something to try):
Download "Cookie" -- it's free to use for 15 days.
Install it and set it up
Set it up to delete ALL website data from your browser each time you quit
- tracking cookies
- non-favorites
- cache
- history
- favicons
- webpage previews
- form values
- downloads
- website preferences
See if this can get rid of the phony update message.