Correct - they do not have memory problems. NiCad's (the early rechargables, now mostly used in short duration - high current applications) do.
Li-ion's DO have a finite number of charging cycles. Topping off when it's 7/8's full will use up those cycles. Their energy storage capacity decreases very slowly over their useful life then drops off pretty sharply at the end. They can last years in occasional use, a few months in a production environment. Your mileage will vary.