Let's just get clear, I'm firmly against the cargo-cult version of scrum and sprints that looooots of companies and teams are applying.
To get back to your initial question about how you reconcile sprints, and more largely scrum, with the agile principles, it's actually pretty easy to do if you take a bare scrum and the principles themselves*
1. And 4. Customers are more satisfied and involved when you ask for guidance and feedback, i.e every two weeks when they look at what you did and tell you what is next
2. Welcome changing requirements - when you lock scope every two weeks, instead of at the beginning phase of a 6 month waterfall plan, this is checked.
3. 7. Continuous delivery - sprints are supposed to finish with a new version of the software that offers more features.
6. Face to face interaction through including business into demos and planning at leasing every two weeks.
And so on.
But.
The *moment* you depart from initial intent, it all goes through the window.
You commit to delivering a feature 6 months from now - you're done.
You stop delivering working software every two weeks, you're done.
Management starts interfering with roadmap, architecture, estimates and work method, you're done.
You insert pms and pos and layers and layers between the dev team and customers, you're done.
Etc. And of course scrum has been received by a layer of people who were used to working with a certain degree of control and certainty and tried to bring that back in scrum, which ended up making it worse than waterfall on all aspects (except maybe PR because no-one wants to sign up for waterfall).
Instead of taking a step back, thinking about what they need, and picking tools and practices that serve them, teams end up taking the thing as a whole, setup all the planning and grooming and demos and retros and blindly without a glance back, forgetting to apply any ci.
Can you reconcile agile and scrum? Yes. Should you "do scrum", fuck no.
* http://agilemanifesto.org/principles.html