Don't they have to legally generate a statement if you had activity? Say I run 2k through card and when statement was about to cut I just login and pay in full (say im in airport and just login on mobile app). When I get statement in mail/email I notice that I had a charge for $100 that wasn't mine.

Don't you need a statement to check these things? (I know with bank statements you typically have 30 days after you receive statement to contest a charge). When would this period start if u never receive a statement?