Not sure if you're disagreeing with me or saying the same thing in a different way. If you have a barometer that reads true, uncorrected barometric pressure, then yes it should be the same thing. I certainly don't, and when I see "barometric pressure" given in weather reports (not talking AWOS, but news outlets, TWC, etc.) it's corrected to sea level and will be in the 28-31" range even at high altitude sites. That's why I said "ambient barometric pressure at sea level, minus 1" per 1000 feet".
I don't have a commercial barometer to check at the moment, but my Dad's (long gone) was designed to be calibrated to agree with sea level corrected pressure. I assumed that all barometers in common use were that way.
Also: although the definitions are certainly different, there is usually little difference between barometric pressure corrected to sea level as given in news reports and altimeter setting. In fact, I think most of them just use the altimeter setting from an ATIS or AWOS.