Are we really and truly capable of completely forgiving someone who has wronged us as if they never had? Or do we carry a grudge, albeit a very tiny one, to the grave?

It depends of each person.

Yeah, you can truly forgive and should. That doesn't mean you have to forget or allow them back in to do it again.

Some people forgive more easily than others. People who have intense emotional natures that react with deep hurt when offended are the ones who carry grudges for the longest time.