the reason people say the weld is stronger than the metal you are welding,, is generally with mig welding you only heat a localised area which cools fairly quickly and it tends to make the surrounding area brittleerm a good weld will be as strong as the parent material, a way to test (off the top of my head) if my college days serve me right is called hounsfield test, which is basically a strech test, if the weld snaps you've c**ked up in simple terms
another form of weld testing (this is actually a recognised form) is actually destruction testing aka smack fook out of it with a hammer!
i wouldn't say the weld will be stronger than the parent material, it will be as strong