Scrum and Agile are loosely-defined. Every company implements it differently depending on how much they can "tolerate." I've worked on projects where we don't use sprints, and other projects where we break down stories to hourly items.
The best way to implement it is to use whatever practices benefit you, and leave whatever doesn't. While some "puritans" may complain that it's not scrum, reality dictates that unless people get benefit out of it (or see benefit in the process parts of it) they won't want to implement it.