This wouldn’t work. Microwaves simply make the water molecules vibrate a lot, and the more they are vibrating, the hotter the water is. Microwaves at the energies present in consumer and commercial grade ovens cannot change the chemical or nuclear structure of water at all, much less to the extent that it would be dangerous to anything. But, machines malfunction? Maybe somehting could go wrong that would do this?
Hydrogen peroxide can be created from water through electrolysis with specific electrode materials. But this requires a very careful, deliberate setup. So while microwaves can induce currents in conductive materials, this isn’t something you can do accidentally in a microwave.
The other possibility I could almost see would be creating radioactive isotopes of the hydrogen and/or oxygen. This requires a hideous amount of energy. Knocking neutrons out of the oxygen might do it, especially if some of these neutrons are captured by the hydrogen. To do this with small, very stable atoms, requires a hideous amount of energy- especially so when the beam is not focused specifically to the oxygen nuclei, and in fact has a wavelength so high that proper focusing is fundamentally impossible. No consumer or commercial grade oven is capable of handling this sort of power- they would literally melt down/explode if you tried to send that much through.
But hey, maybe you have a super oven that can handle that much power running through it. At this point, you’ve got a plasma going on. You are breaking up oxygen nuclei. You have hydrogen floating around that’s long since separated from the oxygen it was bound to. Nuclear fission + free hydrogen = hydrogen bomb.
So basically, if this urban legend was real, the water would never hurt the plants because the person boiling the water would have been killed in a nuclear explosion.
Now, as Snopes said, contamination of the water, its container, or experimental error all could have created the appearance of something bad going on. Also, there could have been contaminants in the water that, while not in themselves bad, react under the presence of heat to create a plant poison.
But the water itself? If it survived to be given to the plant, it’s not the problem here.