If you read the links you posted you woudl have seen this. Only usage based plans are covered so only those tiered plans are covered by this free hot spot since you are paying for the data already it should not matter how you go about using it.
The difference on the grandfathered unlimited plans also is that Verizon will not subsidize the cost of phones......which means that you don't buy a Razr M for $99 (example)....you pay full retail price.
Last month I bought a pair of Razr M's ($149 for both phones) to replace the D2G's my wife and I had. I needed to move off a 3G plan to 4G LTE service. I was offered to keep my unlimited plan IF I wanted to pay full retail price for my phones...I didn't want to do THAT. LOL
I switched to the new Share Everything plan. My wife and I don't do much data (wifi is available for us a LOT) so hitting/exceeding a cap wasn't a concern. But we had just cut the cord on our house landline so the new plan's unlimited talk was attractive. We chose a 4GB a month plan and our cost went down about a buck a month. And now...I can tether if I want without paying the extra $20. I seldom tether, but if I'm going on vacation and need to...I can bump up my plan to a higher cap for that month so I don't exceed my cap.
Verizon can still make it a pain for you. You're getting that message app because you're using the built-in tethering or an app that just enables the built in tethering which Verizon modified. There are apps out there, like FoxFi, that do tethering on their own. You can do this over USB, Wifi, or bluetooth. With the current version of Android on a Razr HD FoxFi will work fine to share your wifi but it does require using a certificate, which it will install, and as long as the cert is installed it forces you to use a lock screen - which is a pain. That must be a moto thing. It doesn't do that on other devices like the GS3. I don't think it does that if you use USB tethering. So you say, well how is this better than it was? Verizon used to actually block tethering apps in the store and threten you if you used them saying you're breaking the law or something. They legally can't do any of that now. It's perfectly legal to use a tethering app and Verizon can't even block them on the Play store.
I've rooted my phone and am now experimenting with other tethering apps but none of their SSIDs show up in Windows. I've tried Wireless Tether and Wifi Tether so far. No luck with either.