Put simply - yes, your book is wrong. Very wrong. The general rule of thumb, esp. for beginners is 1 inch of fish per gallon, allowing for their full sizes. This gives each fish ample swimming space/territory (for a non-aggressive species - aggressive fish need more room than usual), plenty of oxygen, not too heavy a bioload (not too much fish poop for the amount of good bacteria that will get rid of it), & leaves you with a little room for plants &/or decorations. 22 2 inch fish is 44 inch of fish in a 15 gallon tank, which is very overcrowded, which makes fish a lot more suseptible to stress/bullying & disease.
With very vigilant water changes & maintenance, you can go a little overy this limit, provided that the fish are an approximately even mixture of bottom, middle, & top dwellers, but for a beginner I wouldn't really recommend it (I still stick to it pretty much too with my 15 gal). A couple more cories will be ok, & your current guy'll be happier, but anything more than that I'd say would be pushing it. I don't know where your book got it's info but that part's definitely wrong.
Hope that helped. Michelle.