There should never be a battle or a bargain about food.
As a parent you decide what food should be available to your child and allow them to choose from it what to eat.
If she was full from a very large lunch and a fairly recent snack a piece of fruit was probably a very appropriate meal. Her body was telling her that and you decided to tell her not to listen to it. Not a great move.
What do you think you will achieve by insisting that she tries one mouthful? Toddlers are instinctively resistant to 'trying' food. It's a natural mechanism to keep very young children safe from poisonous foods. Forcing her to try something now won't make a jot of difference to what she eats in years to come, unless you make such a hash of it that she ends up with major anxiety issued around food.
I completely get the idea that a child cannot live on fruit alone and that their diet overall needs to be balanced. However, each individual meal does not need to be balanced. If you took her food intake for that whole day, including just fruit for tea, you'd probably find it was exactly the balance you wanted.
You need to take a step back from her eating. Put the food out at meal times, allow her to eat what she would like, take it away and put a sensible amount of fruit out. If she wants more fruit than you think is reasonable suggest that she has her main course back instead as it will still be palatable after such a short time. If she doesn't want it that's fine. She can leave eating until the next meal.
Don't deliberately deny children one sort of food as a punishment for not eating another. That makes no sense and turns the whole thing into a battle for supremacy which the child will inevitably win. Just don't allow them to change the balance of their diet as a whole by filling up on the thing they like best.
YANBU to allow your child to be a bit hungrier by the next meal. That helps them to enjoy that meal more. You did the right thing by allowing her to have her milk. Hunger should never be a punishment.