Vacuumdevil is right. The Kirby shampoo system is only a surface shampooer and not a deep clean shampooer. It's ideal if you want to keep your carpets clean and fresh every 2 or 3 weeks and fluff them up, but it doesn't have the capability to really get down to the backing and suck dirt out.
I have used Bissell's shampoo in my Kirby shampooser before and haven't had any issues in it, but I do know that some chemicals will eat away the hose rubber and weaken it over time by drying out the rubber. Happened to my ancient Bissell shampooer from the 1990s.
The Bissell ProHeat Pet is a more economical and simpler choice than the Kirby if you really want to do some deep cleaning.
You do have to use Kirby brand shampoo though to answer your question, that's no sales hype, it is true. Kirby formula is a special dry suds system and its been specifically tailored to the Kirby equipment and its foamer system.
Try shopping around more and looking for cheaper retailers, or look for old stock from years ago you might be able to get cheaper due to its age. I still have the Kirby shampoo from when I bought it in 2002, but there's just a tiny bit left of it.