what makes them claim that bitcoin cash is the "original" bitcoin? what basis could there be to support that claim?

technically, i think the original bitcoin was the version created by satoshi nakamoto - the very first version, the version without iterations. when that version of bitcoin went through iterations and forks, then the original was changed.

however, since bitcoin follows certain consensus rules, and a bitcoin consensus - or a general agreement of what is called bitcoin by a majority of participants, then forks that deviate from these rules cannot be referred to as bitcoin. since bitcoin cash digressed from bitcoin's consensus rule and bitcoin consensus, then it was not awarded the bitcoin name.