Interesting. I was definitely wrong about my assumptions before. My bad. I don't personally use that weight tool for anything (I use the spreadsheet) but I can see the issue happening in your video. It's not clear though just how blue those verts are.
When you select one of the blue verts, what is the weight value on it in Abs. Effect? If it's very low, like .008, why not just use the "Remove Zero Limit" and "Remove Zero Weights"? (Removing 0 weights is similar to manually right clicking Abs. Effect.) It would save you a bunch of time that way. Setting the limit to a low value and clicking the button will automatically do what you're doing in this video for all the bones and verts in the model. Save first, of course, because it takes some trial and error to find the sweet spot.
Or, instead of clicking on the 0 value in the weight paint tool to remove the weight, can you try right clicking on the Abs. Effect button? (Found on the "Weight Properties" rollout. If you do that instead setting the values to 0, does the problem go away? (Again, a weight of 0 and a weight of N/A aren't quite the same thing. You may have luck with it.)
Another thing you can do is use the Bone Affect Limit to prevent bones from affecting verts far away from themselves. I use 4 for video games, and 6-8 for high end models. The default of 20 is overkill imho. Setting that may also solve your problem without you having to go through what I can only assume is a tedious process for every bone and vert.
But one thing we can both agree on is that verts you zero'd out are turning blue again. I am now a believer.
Best Regards,