Does MFP include fiber in the carb calculation?

You probably wanted a simple answer. There isn't one, IMO.

In free MFP (without the net carbs feature), MFP just adds up the carb and fiber entries from the foods you choose from the MFP database and put in your diary.

The database is crowd sourced: Entered by regular users like you and me, most often using the data on the food label. MFP users are in multiple countries. In some countries, IMU the labels include fiber in the carb count, and in other countries, they don't. That implies that some MFP food database entries include fiber in the carb count, and others don't. On top of that, some MFP users don't much care about nutrition, or aren't very good at typing, or something, and they don't enter the right data from the food label.

If you have MFP premium, and activate the net carb feature, MFP will show you net carbs by subtracting fiber from carbs and showing you a net figure. However, it will do that based on what's been put into the food database entry, which may have fiber included in the carbs, or may not, and may be incorrect for other reasons.

So, there's no answer to this as a "does MFP . . . " question.

Those of us who care about accuracy choose our food database entries very carefully at first, making sure that the values we personally care about are accurate. You can do that with carbs and fiber.

As long as you keep eating those well-checked foods regularly, they'll be in your recent/frequent foods, and come up first when you go to add a food to your diary, so you'll need to do less checking over time.

This is not a special hurdle for those trying to eat low carb. Anyone who cares about the accuracy of calories, protein, whatever - they should do this checking at first.

There's nothing magically correct about the green-checked foods: It's that several MFP users have agreed that the database entry is accurate. It could still be inaccurate, or it could be from another country, etc.

For foods without labels, you can check against the USDA FoodData Central database:

https://fdc.nal.usda.gov/

Usually the SR Legacy category is the most helpful.

When MFP was first started, some foods were loaded from the then-database at USDA. That's a small subset of the huge MFP database now, but most of those entries are still accurate. If you find the full name of a food in the USDA database, you can try using that as a search term on MFP. They tend to have names only a bureaucrat could love: "Tomatoes, red, ripe, raw, year round average" "Peas, split, mature seeds, cooked, boiled, with salt". The default serving is usually cups, but in the drop-down list there will be multiple types of servings, such volumes (quarts, liters), weights (pounds, grams), sometimes inch sizes or per-piece. (User-entered items may have different servings, but they're all the same type, such as grams, ounces (weight ounces, not fluid ounces).

Those are usually good entries, and after a while I got good at finding them without going to FoodData Central first. If an item in the MFP database has "USDA" in the title, it isn't one of those entries, it was user-entered. I find the initial-load ones by guessing at the bureaucratic name, which often works.

Like I said, probably not what you wanted to hear, but that's the situation as I understand it.

There are apps that have only their staff enter foods in the database. They tend to be more accurate, but not contain very many foods. MFP made the opposite app design choice, to let users enter foods. As a result, the database is huge, it's rarely necessary for a user to enter a new food, but only some of the entries are accurate, and it can be challenging at first to find them.

It's a design tradeoff.