http://www.irs.gov/Retirement-Plans/Plan-Participant,-Employee/Retirement-Topics---Vesting
http://www.401kplanning.org/vesting/
http://moneyfor20s.about.com/od/employerretirementoptions/f/Vested401K.htm
http://retireplan.about.com/od/401kplans/a/vesting.htm
http://www.smart401k.com/Content/retail/resource-center/retirement-investing-basics/company-match - this one specifically states the vesting period doesn't restart with each employer contribution.
All of these specifically state you, as the employee, are vested at a certain time (the company has to at least meet one of two types of vesting schedules, it can vest the employee faster, but can't do it any slower than either of the two schedules - cliff or graduated).
None of mention anything about each employer contribution having a vesting period.
All the companies I worked for matched my contribution each paycheck, the matching didn't roll forward with its own vesting period, once I was 100% vested, it was mine.
When I was 100% vested, all of my 401k was able to be rolled over to an IRA, or even into my new employer's plan if I quit my old employer. None of it was held back. No waiting period. That's why I'm confused by the explanations given by you and Rum Tum Tugger. Everything says you, the employee, have a vesting period to be able to claim the employer matching as yours, not that each employer matching contribution has a vesting period.
At least in the case of this thread, post 46 indicates the issue has been addressed satisfactorily by HR.