I have not found the Vz tests to be inaccurate. They do tend to perform better than speedtest.net / ookla, etc. but that's due to being "on network" vs thru the open internet. You are right however about the the Gig service being "up to" vs "guarenteed". Prior to moving to Gig, I would consisently get 100mb (on my 100/100) or very close to it from various test locations on the internet. My Gig connection varies from close to the 940/880 numbers at certain times in the evening to about half that early in the evening and certain other "prime" times.
Some things to investigate however:
1. Browser based speed tests on connections running above about 200mb are not reliable (depending on the browser, it can't keep up). Many speed test sites have an app for testing higher speed which you should use.
2. Vary the test site being used and don't always assume a local one will be faster. Sure it might have lower latency, but it may also have a slow link. A couple of smaller locations which my speedtest.net site seems to favor always max out around 100mb regardless of the speed (that's they're end, not mine). Also, pay attention to who you test against -- not saying anything funky is going on -- but is there motivation for say a "Comcast" run test server to favor speedtest traffic coming at it from a FiOS network? I also sample several sites when testing. YMMV.
3. Seriously pay attention to local congestion on your network. I use Tivo and the remote set top boxes utilize the main box for all content including live TV. Even with the TV turned off, these can each suck up 30mb/s in streaming content on the local wire.
4. Test connected directly to the router which is connected to the ONT. No intervening network hardware (MoCA repeaters, powerline adapters, etc.). These all impact bandwidth.
5. Make sure you system is tuned for high speed / low latency connections (window size, retry times, etc.). There are utilities on DSLreports and other places you can run which will adjust these (newer OS's do a better job at doing this automatically).
Just some thoughts.