Each language has its own distinct grammar. "English grammar" is a description of the way the English language is used. A reference book describing the grammar of a language and presented in a "rules" format is called a "reference grammar" or simply "a grammar".
A fully explicit grammar exhaustively describing the grammatical constructions of a language is called a descriptive grammar. This can be contrasted with a prescriptive grammar, which tries to enforce some hypothetical governing rules about how a language should be used.
It is probably inevitable that English language coursebooks created for the instruction of non-native speakers will be well into the prescriptive side of the descriptive/prescriptive spectrum. Teachers should be aware that the grammatical explanations presented in such books are explicitly simplified for consumption by non-native students and may not always represent the whole truth.
Nevertheless teachers who have to work from a coursebook should be careful about criticizing it to their students as this may cause them to start to lose faith in all the material in the book, a consequence which would impede their learning.
For teachers themselves, Swan speaks highly of The Cambridge Grammar of English, by Carter and McCarthy; The Comprehensive Grammar of the English Language (Longman, 1985) by Quirk, Greenbaum, Leech and Svartvik; and The Cambridge Grammar of the English Language (CUP, 2003), by Huddleston, Pullum et al.