There are two easy ways to influence the editing when you are being interviewed by a journalist.
Make it clear what your key point is
Add a flag when you are about to make your key point. Flag? 'Here's the main point', 'There's one thing I want to emphasise...', 'The real issue is...' and 'Let's put this in perspective...' Reporters will know what you're doing - which is no problem because they might well agree and will at least record it for a later decision.
But we prefer a more subtle method...
Match the interviewer's intensity
If the interviewer says in an indignant tone: 'Come on, admit it! You've handled Mrs Smith's case disgracefully!', you raise your intensity to match his. (What's intensity? Think energy level, or keenness to explain - but not aggression.) 'Certainly not,' you might reply 'The law doesn't allow us to do it any other way'.
Never try to match aggression with aggression or sarcasm or a put down - or that's all your audience will remember about you.
Can I influence the editing after the interview?
For a soft feature story, yes. For a hard news story, no. You're wasting your time. That's the reporter's job and you'll be rebuffed if you try to take it over.