If the B/R reached "first base safely", how could he be out on appeal? The successful appeal shows that he didn't reach safely.
Maybe this will help: From OBR
Rule 4.09 Comment: APPROVED RULING: No run shall score during a play in which the third out is made by the batter-runner before he touches first base. Example: One out, Jones on second, Smith on first. The batter, Brown, hits safely. Jones scores. Smith is out on the throw to the plate. Two outs. But Brown missed first base. The ball is thrown to first, an appeal is made, and Brown is out. Three outs. Since Jones crossed the plate during a play in which the third out was made by the batter-runner before he touched first base, Jones’ run does not count.
This ruling illustrates a couple of things.
1) When a missed base is appealed, the out occurs at the time of the appeal.
2) But if the third out is a force or if the B/R was "forced" to first, scoring is not a time play.