To confirm, I think these birds are unlikely to be escapes.
Assessing escape likelihood is often rather difficult, and as has been implied here, if these BH Buntings are consistently showing plumage damage, then that may have implications for the assessment of other species.
However, assessing escape likelihood should be based on a combination of criteria, and this includes pattern of records and status in the trade. Pattern of records is most difficult to interpret when you are dealing with extreme rarities, when by definition; there is no pattern of records. In such circumstances, regional distribution, moult pattern, and status in the cage bird trade are also important, as are age, and sometimes, sex.
In the case of BH Bunting, given the range and what we know of the cage bird trade, it seems most unlikely that there are any in the trade in China. Even if there was a small wintering population in Yunnan (for example) the chances of these birds being trapped and released or escaping in HK in small numbers (up to ten per year) every October and November must be very slim indeed.
Also, if you look at a map, birds migrating from the breeding grounds to the wintering grounds (which are largely within the Indian subcontinent) which were to overshoot would end up in S China.
However, if these birds are indeed wild, then the wear and tear they show is rather exceptional. Certainly none of the eastern Palaearctic buntings we routinely see in HK show such wear. This is in large part due to the fact that adults do not have a post breeding moult before migrating (whereas most migrant passerines do) and I would guess, in part due to the more arid environment in which BH Buntings breed which is likely to result in more bleaching and abrasion of feathers. Why first-winter birds might show such damage (albeit to a much lesser extent) is more difficult to explain, but environment may play an important part.
Hawfinch, on the other grounds is entirely different. Adults undergo a complete post breeding moult, it is common in the cage bird trade, and the pattern of records is less clear; accordingly any suggestion of cage damage is potentially far more significant.