Space debris and meteoroids (they become meteorites when they hit the Earth) differ significantly in velocities with respect to the Earth. Space debris are more predictable since their trajectories have been tracked for years, using space and ground sensors. Even very small debris' location can be estimated by orbit propagation tools. Since man-made debris are orbiting the Earth their speeds in LEO are between 7-8 km/s (ISS speed is 7.8 km/s). Since their trajectories are known, we can say with high confidence what would be the most probable incidence angle and velocity of the impact at a given moment. According to this NASA study (figure 7-3) the highest flux of space debris, experienced by spacecraft in orbit of 57 [deg] inclination, is for debris with relative speed between 8 and 14 km/s. Similar results would apply to the ISS which has orbit at 51.6 [deg] of inclination.
Meteoroids on the other hand are more of a wild card. They can reach much higher speeds. According to this ESA article, impact velocity of space debris can reach 15 km/s of impact velocity, while meteoroids up to 72 km/s. Although they can be tracked as well, meteoroids can be also sporadic. It means they can arrive from random unexpected direction. Check out section 7 in the NASA document for more data on debris and meteoroids, and how they are modeled.
Therefore, a general approach to find the source of damage would be following:
- Analysis of photos and footage of damaged parts. Size and depth of deformation caused by the collision can be used to estimate velocity and size of the impacting object. It can provide you with a rough idea of what you are dealing with. If the impact velocity was small enough then the meteoroid/debris could be probably captured on camera. Then the estimation would be even more accurate.
- Velocity check. If the estimated impact velocity is huge (let's say above 20 km/s) then it is easy to determine that the source of damage was a meteoroid. Mostly because the likelihood of space debris having that much velocity is extremely small. Otherwise, if impact velocity is smaller you would have to keep digging.
- Incidence angle/direction check. For smaller impact velocities, it would be necessary to analyze the direction from which the object hit the ISS. It could be estimated from photos of the hole/deformation. Then, based on known orbits of space debris it would be possible to compare them with direction of the impact. If they would match the damage would be most likely caused by space debris. However, even then it wouldn't be a certainty since small meteoroids could be in similar orbits as space debris.
To summarize, the biggest factor in determining the cause of damage would be the magnitude of velocity of impacting object. Most likely, Russians estimated a high impact velocity and they quickly concluded that a meteoroid hit their spacecraft.