I'm curious, do you consider English grammar simpler than German? (The few people I've talked to about linguistics consider German to be a harder language for English speakers to learn than Spanish, which seems like it must be due to grammatical differences...)
English is a MUCH easier language grammatically than German. Just the fact that German has gender assignment on words increases the complexity of the German Grammar by a large amount.
Chinese is a very strong counterexample to your statement based on your definition of "complex grammar."