The reason finger counting is discouraged is because it slows down the whole calculation process. Fast recall of of arithmetic facts are essential for questions from "There are 8 eggs in a basket and 3 are taken out. How many are left?" through to "Solve 7x + 3 = 52" and beyond.
Yes there are calculation methods which use the fingers to work out calculations at super fast speed, which is great if you're going to train your child to do that but leaving your child to finger count while her classmates move ahead because they have memorised the arithmetic facts is just not fair.
Try starting from the basics, memorising +1's first, then +2's , then +3's. I talk in more detail about this on my blog
The only reason I see that the OP's DD should not use her fingers is that she almost certainly has an already well developed number sense and was able to manipulate the numbers in her imagination. Being able to see math problems in ones imagination is one of the things that sets those who can really do higher (and I'm talking about beyond a very basic algebra problem like 7x + 3 = 52) math from those who just go through the motions. If the OP's DD in reality has simply memorized the addition, then I would actually encourage finger counting to help her develop number sense.