我汉语说不好 could be misleading in some way.我的汉语不好/很差 understandable
我汉语说不好 much better
Textbooks can be very wrong, but I know so little Chinese that I can't tell if they are wrong. Haha.Not saying that your textbook is wrong, but me and my friends do believe that "很" has a real meaning here. And according to #4, you can see that there's obviously another native speaker who took "很" as "very" in the sentence.