The VLSS issues I've seen have more to do with how it's implemented at VZ than anything else. It was originally implemented because too many projects were trying to solve problems by attacking the wrong root causes. LSS forces them to use data to prove what the actual root causes are which allows the correct issues to be focused on.
Unfortunately for VZ they want everything yesterday and/or immediately, so using a methodology like LSS which requires discipline and time will not work. I've heard several LSS people say that they don't do the DMAIC part of a project because they are told to go faster, which means they are approaching problems just like they did prior to VLSS starting.
It's a vicious circle, and unfortunately most of the problems VZ has are related to antiquated systems and processes that are very expensive to fix as well as the company just flat not having any resources (due to layoffs mostly). VLSS won't/can't fix those types of issues, but those are exactly the types of things they are being tasked to fix.
I feel for many of the people who will be affected. They came into that program being told it was to develop the company's best and brightest, but when their two years in the program is up there aren't any positions for them to move back into the business.