So far I have had experience with hybrid models only :-) None of the agile projects I have worked on so far implemented any Agile methodology strictly by the book. You needn't either.
The point is, any methodology is just a starting point / a collection of ideas you can use to work out your own process, tailor made to the specific project, team and circumstances.
Start with a process which looks good to you, then see how it works in practice. Keep regular retrospectives at the end of each iteration to assess how things are going, what worked in the last iteration and what didn't, and how could you improve things further. Then implement the most important ideas in the next iteration. In other words, develop the development process itself in an agile way :-)
Update: anecdotes about the requirement process
As I write this, I realize you may not got much useful info out of it... but at least it shows you that projects and processes vary a lot.
In one project, we had a fairly strict Scrum process, with a product backlog, although we didn't have a real customer: the product was new, and the prospective users didn't yet know it existed. Also it was a fairly specific and standardized domain where our company had a lot of experience. At the time I was part of the team (this was before the first release) we didn't really have much formal requirements gathering, because much of the key requirements were imposed on us by a standard. On top of that, we had some of our own ideas how to make the product stand out of the crowd.
In another project, we loosely had a Scrum process, but our sponsors and users did not really know about it, so we were struggling quite a bit. The "requirements gathering" was rather informal in that the product was huge and different people / subteams were assigned to different areas, working fairly independent of each other. Each subteam had their own contact(s) to discuss the requirements with, and the contacts were geographically separated - we rarely saw any of them face to face, so most of the communication happened via email, using lengthy Word docs. To top it off, we had a team of domain experts, who were often in wild disagreement with the users regarding the concrete requirements, however they were not very communicative. So the requirement process often consisted of reading lengthy documents containing obscure mathematical stuff, then other lengthy documents containing GUI requirements, then trying to figure out how to bring the two together... then discussing the requirements with the domain expert who briefly announced that it was a piece of sh*t, and we tried to tease some more useful and concrete improvement ideas out of him... then rewriting the requirements doc according to our latest understanding and the expert's comments, and sending it back to our contact person... then repeat from square 1.
In our current project, we again have many users scattered around a large part of the globe. However, at least our IT management is more knowledgeable about SW development and agile processes. We work on a large legacy system, which was in a pretty bad shape a couple of years ago - so maintenance and stabilization is a large part of our day to day work, and new requirements take less than half of our time on average. When we have one, though, we usually have preliminary estimation meetings where we try to come up with a crude estimate on how many person-days this project going to take. Then later our business analyst works out more and more details with the stakeholders, and our team works on filling out the technical details.