What she says in this speech is 100% true. God puts us where we are for a reason and He uses our flaws and weaknesses to help others and glorify Him. It is easy for someone who looks great and has no problems to say, "God is great." We don't pay much attention to them when they say how God did great things for them. But when a person who struggles through life talks about how great God is and focuses on the great things He does for them and encourages us to put faith in Him, we tend to listen. Here is a person who has gone through so much hurt and pain. How can they be so strong, positive, and happy? When they reply, "I am not. What you see is God's strength in me", that is powerful. Doesn't that make you want that strength? That is one of many reasons why God uses the weak.
If you are picked on because of a weakness you have, let it go. Know that God created you for a reason and He is using that weakness for good. Know that you are cherished and loved by Him and He is in control. If this woman can get through life by relying on God, so can you.