"how honest is the Chinese claim of quantum supremacy?"
It's equally (or at least as) honest in comparison to Google's claim.
In a comment to this answer at Quantum Computing Stack Exchange, Craig Gidney (who works at Google and was a co-author on Google's Quantum Supremacy paper), confirmed that the classical computer would have been
2^(20*7/4) = 34359738368 times faster if Google's hardware used CZ gates instead of their gates. This would mean that the 10,000 years that they said it would take classical computers to do the calculation that Google did, would become 9 seconds.
Furthermore IBM pointed out that the estimations Google made about the time it would take the classical computer, assumed that the classical computer could only use RAM and no disk at all, and if you allow the classical computer to use disk (which in this case, since they used Oak Ridge National Lab's Summit supercomputer, has petabytes available rather than just terabytes) then even though I/O is slower on disk than RAM you will save so much time by not re-calculating things, that you will get several orders of magnitude further speed-up for the classical computer.
I'm not aware of anything like this for the Chinese experiment, but to be clear: boson sampling is not enough to do "universal" computation, however universal computation is not a requirement for quantum supremacy. The probability distribution from which boson-samplers sample, is #P-difficult to calculate on a classical computer, which means that no polynomially scaling classical algorithm is known to be able to simulate such a distribution. Discussions have taken place on the Quantum Computing Stack Exchange about whether or not boson sampling can be used to "calculate" the permanent of a complex-valued matrix (this is known to be a #P problem for classical computers), for example.
Furthermore, Figure 1 of this paper shows that it wasn't hard for the authors to simulate 144 qubits on a classical computer. That paper was published 1 year earlier than Google's quantum "supremacy" claim! This was discussed in more detail here.
In any case, "quantum supremacy" is a buzzword and until people are actually using quantum devices to solve useful problems, classical computers are superior because people actually find them valuable enough to purchase.