The kindle device logs quite a lot of info. A registered kindle device connected to the internet talks to Amazon servers quite a bit. Yes, those local logs could easily be pushed/pulled to Amazon servers. Yes, those frequent communications are encrypted. However... after much scrutiny, experimentation and network sniffing, no one (to my knowledge) has actually caught the kindle "phoning home" data of any size that would indicate log files (or even portions of log files) are being transmitted in these encrypted communications while the device is at rest. They are pretty-much the size of most "keep-alive" pings.
In short: yes... I think Amazon could easily access log files on your device without you knowing. But most evidence suggests that's not what's happening.