That's a bit strong. A lot of the tanker fleet is in the reserve, but not "almost all". Many of the Air Guard units in particular, and some reserve units too, have converted from other missions, such as fighter, interceptor, recon, etc, to tankers in the past decade or so.
Will defer to you on this, I just used my impressions, not firm facts. Seems like the reserves are really integral for refueling such that the Active couldn't get it done without them. But as I said, that's just my impression. I'll let any zoomie give the true story.