Here is the only mention of the possible age of the comet. It is a statement without any backup data, source or logic. They are simply making the assumption the comet has been around billions of years. There is no way to tell how long it has been around by looking at it. The only thing we can surmise is its orbital period. It could be on its 1500th trip in to the Sun or its first. It has probably been around since the beginning but that's just my guess. So the answer to your original question is "they fit the comet to the age of the solar system".
"The Oort cloud's comets were tossed out of the solar system billions of years ago by the gravitation of the massive outer planets, according to Jewitt. "
You are on the right track here, unfortunately, the problem is in the published paper too.
Hubble Space Telescope Detection of the Nucleus of Comet C/2014 UN271 (Bernardinelli–Bernstein) - IOPscience
"1. Introduction Long-period comets are considered to be compositionally some of the most pristine leftovers from the early solar system. For most of their lifetime, they have been stored in the low-temperature environment of the Oort cloud, at the edge of the solar system (Oort 1950). Recent years witnessed identifications of several long-period comets active at ultralarge heliocentric distances (rH ≳ 20 au), implying that the long-period comets may be more thermally processed than previously thought (Jewitt et al. 2017, 2021; Meech et al. 2017; Hui et al. 2018, 2019; Bernardinelli et al. 2021). Unlike most comets that are only active within the orbit of Jupiter (rH ≲ 5 au), driven by sublimation of water ice (e.g., Whipple 1950), the cause of activity in distant comets remains unclear..."
As you stated very clearly, *So the answer to your original question is "they fit the comet to the age of the solar system".*
Reporting like this gives the impression that the radiometric age of meteorites used to establish the age of the solar system, determined by Clair Patterson in mid-50s to be some 4.56 billion years old, is a non-falsifiable age for the solar system, my opinion. There are many objects documented today in the solar system that show much younger ages like the lifetime of comets in the solar system. Young ages reported for different objects in the solar system (even short lived asteroids) are simply fitted into the accepted age model.