It's the other way around. The evidence doesn't depend on the assumptions, the assumptions depend on the evidence.
The observations are very good and offer little latitude for interpretation -- there is a very massive, very dense object at the focus of multiple stellar orbits near the center of our galaxy, and both the mass and the density of the object are easily and unambiguously derived from the orbits.
It's the same with other galaxies -- a massive, dense central object dominates the orbital dynamics of the galaxy near its center. We're obviously not free to say that means black holes exist, it's just another piece of evidence. But it's a way to exclude certain alternatives.
Maybe it could be worded better. In order to say that gathering this evidence is the same as directly observing a black hole, we have to make several big assumptions.
The observations are very good and offer little latitude for interpretation -- there is a very massive, very dense object at the focus of multiple stellar orbits near the center of our galaxy, and both the mass and the density of the object are easily and unambiguously derived from the orbits.
It's the same with other galaxies -- a massive, dense central object dominates the orbital dynamics of the galaxy near its center. We're obviously not free to say that means black holes exist, it's just another piece of evidence. But it's a way to exclude certain alternatives.