I was going by the way my 7D works, that also says live view, silent shot and video. I'm sure it is the same in all shooting modes...
I believe it applies to Live View only. Keep in mind that in live view and movie modes, the mirror is up and metering is done off the main CMOS image sensor, whereas with VF shooting the dedicated metering sensor in the pentaprism housing is used. It's logical that the settings would be different.
I don't think it's possible to change the time metering remains active on the 5DIII, or any body outside the 1-series. On the 1D X you can fully customize three separate time-outs from 1 s to 60 min – metering and AE lock (default is 6 s), FEC and multispot metering (default is 16 s), and metering after shutter release (default is 2 s).
Any idea how many seconds the metering timeout is in viewfinder mode on the 5D3 if i tap and let go of the half-press shutter or AF back button? Is it 2 sec like the 1D-X?