Update:
So, @Jos_Naabal and @Cellulanus in Discord has raised a point that The Order might have scanned Jacobi on Osiris after the rescue, which is possible.
However, since Osiris is a stolen experimental vessel, it is also possible that the ship is not equipped with systems that allows it to perform health care service. Get cloaking to work is already hard enough and may consume a lot of space and power (claimed in rumours), a hospitals maybe just too extra to install for the experiment.
