The story about the woman's plumbing being ruined by water soluble stabilizer has been floating out there for more than 10 years.
Water soluble means just that...it dissolves when suspended in water. When you rinse out the stabilizer it goes through your pipes into waste lines that take it to the sewer system or septic tank. It will not "reconstitute" inside your plumbing.
Non-water soluble mixtures can, over time, cause plumbling problems. Acrylic paint, bacon grease, cooking oil are all examples of mixtures that are not water soluble. They can and will coat the inside of the pipes and eventually cause the pipes to clog.
Please don't worry about using water soluble stabilizer. ;)