Well, I thought that I would try tinkering some more because it really annoys me that I saw the problem, and wasn't able to reproduce it. (My professional background involves evaluating firmware/software and developing test processes to evaluate product integrity so I do not like leaving inconsistencies like this unresolved...)
This time I only entered "bsecure.com" in the websites to block rather than the full dir-655.bsecure.com, plus another url to see if it was blocked. Personally, I would like to leave the bsecure.com site blocked because I have no use for it. After a reboot I was unable to use any of my usual bookmarks (except the one for the web interface for my email at my ISP which was odd) as the address was not resolved.
Went to blank the blocked sites so that I could report my findings but then I was getting the cycling between dir-655.bsecure.com and loading again! All other sites were blocked! Not even the email site this time! Having already undone all of the changes that I had made to the website filtering, now I was at a loss as to how to restore my internet services.
So this leaves just my router's IP viable. I tried entering just the base dir-655.besecure.com website. The login site appears. Nothing else to do, so I log in. Of course it shows all of the equipment on my network. Nice. Pretty cool that that still gets updated considering that I've disabled it, right? NOT!

There was an option to delete my account, so I used it.
So, to stop SecureSpot you need to:
1. De-select the checkbox in the firmware on your router
2. Turn off the Access Control on the dir-655.bsecure.com website
3. Delete your account on the dir-655.bsecure.com website
...I'm hoping that this is all...

Log off, reboot, things seem normal again. For how long? Any guesses?