Yes, you have the option to share the data with those who have permission to access the JMP Live report. In his Mastering JMP session on collaborating using JMP Live, @HydeMiller explains.
The information button shows 1) which groups can access the report 2) when the report was last updated and 3) a link to the data table if the author has made it accessible. The ability to share the data allows you to use the JMP Live report as a sort of repository of the most recent data, alleviating the need to send the table to others after it is updated.