This is because fetching data from a local machine in PHP on the server is not possible, PHP only knows what it receives in the request, you'd have to send the entire database with every request, which is expensive slow and won't scale, not to mention a security disaster ( anybody snooping gets the entire data set, HTTPS is a bare minimum ). If you opt to go down this route, it would be more secure from both a technical and legal standpoint to just store it on the server
Keep in mind though that this data has to come from somewhere, so users will initially have nothing to work with
During a session, the user can click on members of the list and our system would fetch data of only those, complete the transactions , provide the results and then remove the data from the server.
This implies that information about those people exists on the server. If you want no data of any kind stored on the server, then you're going to need to provide all the relevant data in a request. All a server can do is access external data sources, or process the data and return it ( in which case why not just process it locally )