plants dont have 'stem cells' so to speak. plants contain meristematic tissues, which are the tissues in the plant which are actively dividing and growing. after they divide differentiation occurs, where the cells which were once just dividing cells, start to do different things, like turn into mesophyll cells (photosynthesis) or vascular tissues(transport), etc. etc. the majority of plant cells are also totipotent, that is that they have the ability to de-differentiate from whatever tissue they were found in and can start to divide again like the meristematic tissue and grow what is known as callous tissue. you can control what organs callous tissue will differentiate out into with hormone treatments. the auxins (IAA, IBA, NAA, 2,4-D) will be used to induce root growth and the cytokinins (BAP, kinetin, zeatin, etc.) can be used to induce new plants shoots to grow off the callous tissue which can be cut and rooted into new plants (or roots can be grown in the tc and the plants can be transplanted)
it looks like though that your geek was simply tissue culturing nodes with meristems (shoots) already on them, and not doing tc from a leaf, or pith or some other single tissue culture, but a mixed tissue culture so theres probably just regular nutrients in the agar and no hormones.
and r.e. the pathogens. the theory is that viruses either cannot or do not penetrate into the meristematic tissues of the plants (because if they did they would kill the plant way faster) so you can TC the meristematic tissues and hopefully will clone off virus free growth.
I am only here to entertain the most absurd of ideas