Two billion light years away? Therein lies a good portion of why it ain't so. Why would one assume that distance?
One wouldn't
assume that distance: one would make attempts to measure it. The distance to Messier 106 has been measured, using plain old 500 B.C. style geometry, at 25,000,000 light years, plus or minus about a million. Modern telescopes can pick out individual stars in M106. My pitiful little telescope will let me see M106.
A similar galaxy 80 times further from us will look 1/80 as large, and much fainter, than this one. A supernova that far away, though, can still be detected, and guess what: one out there looks just like one at the distance of M106, except further away! Why should that be, in case after case after case?
It's a little like if I drove over to Big Spring, Texas, down the road from me, and looked west on Interstate 20. You can see about 15 miles' worth of straight highway from a rise there. Very near you, you can see headlights of semi-trucks: bright, even resolved into the driver- and passenger-side lights. A mile back, you just scarcely see both lights, not so terribly bright. Fifteen miles back, you see tiny, faint, single glimmers for headlights. But even though headlights differ some in intensity, you can tell (and could quantify, with a little effort) which are far away. The semis don't start as Matchbox toys, morph to Tonkas, and then to real semis: distance is what makes the difference in brightness and angular extent. The same works for galaxies, and for supernovae.
And then there are several other methods to measure galaxy distances, too. The Highway Patrol only use Doppler shift to catch the local speeders, but every one of those faraway galaxies is speeding.
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