Technically, yes. Just as anyone can call themselves a "personal trainer" or "coach" and start selling their services, so too can anyone call themselves a "nutritionist" and give as detailed advice as they like.
In practice, if you wish to avoid legal liability, it's best to stick to what you're qualified by courses or experience to do. So for a PT, the diet advice can be general only, like the sort of stuff you find on government health sites. I stick to what I call "nutritional first aid." Just as the medical first aider doesn't cure the patient, they just provide a viable body for someone more qualified, so too with nutritional first aid.
"Hmmm, I see from your food diary that you live on cigarettes and KFC. Most people find that if they quit smoking and eat some fruit and vegies they feel better." That's fine.
Or, "if you find it physically difficult to eat enough, many people find it easier to consume more if they just drink milk and eat eggs. So long as you've not some kidney problems or whatever." That's okay, too.
"You should eat 122g protein, 343g carbs and 117g fat tomorrow, then the day after fast and just drink lemon juice in water all day to detox." Not fine, too detailed and specific. Whereas for a qualified registered dietician, they can do that stuff.
The key thing to remember is what the Americans call "scope of practice." That means you only talk about shit you've studied formally or had experience in. For most PTs, that's just exercise.
You can give whatever advice you like about whatever you like, but if someone gets hurt or sick and sues you, well... It's like your house burning down, it probably won't happen but if it does you're fucked. So try to minimise the chances of its happening.
In the end most clients won't need detailed advice anyway. Most people simply need to eat less junk food, drink less booze, and eat more actual food, fresh fruit and vegies, stuff they prepared themselves from raw ingredients at home. Because most people's diets are fairly shit, they live on stuff out of colourful packets. It's like Dan John puts it in
Mass Made Simple:-
Before we get too specific: Eat like an adult!
... Honestly, seriously, you don't know what to do about food? Here is an idea: Eat like an adult. Stop eating fast food, stop eating kid's cereal, knock it off with all the sweets and comfort foods whenever your favorite show is not on when you want it on, ease up on the snacking and - don't act like you don't know this - eat vegetables and fruits more. Really, how difficult is this? Stop with the whining. Stop with the excuses. Act like an adult and stop eating like a television commercial. Grow up."
And we can give that sort of advice without worrying about anyone getting sick or our being sued.
Even if you give detailed dietary advice people won't follow it anyway. Most people don't know how to eat like a grown-up, and become quite stressed at the thought of it. As a professional, for my reputation I'll stick to the stuff I can control: their exercise in the gym. I can't do a thing about the other 165 hours a week if they choose to fuck it all up. All I can do is make sure they do a deep knee-bend, pick something heavy up off the ground and put something heavy overhead, and do more in each session than they did before. Rest is up to them and their common sense.