Although every one of their arguments could easily be proven false, were proven false, the constituents had no say over the matter, especially those who resided in States run by Republican Governors. Even constituents who lived in States where they could sign up for protection against insurance denials of coverage for pre-existing conditions were skittish (or skirmish) about adopting it because of the campaign of misinformation and deception GOP Leaders had engaged in.
The much unfortunate reality is that Republican lawmakers deliberately misled their supporters. They consciously lied to them in order to prevent their support (or adoption) of the Healthcare Act. In fact, in the 2018-midterms elections, the GOP Legislators more at risk to lose their seats ran aggressive campaign ads which promised the Republican constituents protection for pre-existing conditions against insurance rejection of coverage.