Using almost the identical ingredients, I've been making this for years. I DO cook the meats and rice together, and I use packages of those rice mixes called Saffron or Yellow Rice. (Use one that really does have saffron in it.) I saute the chicken, then add the sausage and saute it, then add peppers (red ones make it prettier, garlic and onions. I then add the liquid as called for on the pkg. and cook until 5 or 10 minutes remain. (Using organic no-salt and low-fat chicken broth is good.) Then I top with the shrimp and a cup of frozen green peas, re-cover the pot and cook until done. Well, I suppose my recipe is different, but chiefly in the method, and I felt these ingredients all cooked together needed redeeming because of those reviewers who, rightfully, criticized it as not "authentic" or deserving of the name paella. Try same ingredients with my few changes and additions, and it will taste authentic and it is so easy!
paella's made by frying the rice lightly in the oils of the other ingredients and then cooking in broth, never steamed or boiled. this recipe might be quick but it's not paella.
Please do NOT call it paella because it is not. Rice is always cooked with the ingredients.