As kma88 pointed out, you are confusing Chinese nationality and RTL here. What you said is true for Chinese nationality and Chinese nationality derived ROA, but not RTL.
Though it's possible, if not very likely, that at least one of his parents obtained BDTC status (e.g. through naturalisation before 1997). If that's the case, there should be a record of this somewhere, and if the OP can find it then the OP can prove that the OP holds RTL.
Incidently, I do recall reading somewhere that prior to the handover, individuals from Taiwan (who only had ROC passports and no other status) who lived in Hong Kong were considered de facto stateless (and different from, e.g. mainlanders who had arrived on HK and were considered Chinese permanent residents there). The set of inconviences from this may have made an application to naturalise as a BDTC more likely than it would have been otherwise...
What documents his or her parents used to enter the US?
a British national passport or something else?