This is kind of true, in that (almost) any body type can do gymnastics. There are, however, certain body types that will make gymnastics extremely difficult and make the athlete progress slowly. I would never rule a child out based on their height, as it is not really an indicator as how far they will go, especially at such a young age. I would also not rule out a child based on being too heavy, as I've seen lots of heavy gymnasts be very successful.
I will tell you, completely and honestly, that in my opinion, the kids that have the hardest time with this sport are those that are heavier and not at all strong. Strong kids can carry a little extra weight and do just fine, but if their upper body is naturally weak and they have large frame to support, bars is going to be just so extremely hard, even at the lower levels, it's sure to result in frustration.
That being said, I have a kid that was very good at tumbling and vaulting but had never done bars before. She was a little chubby (not obese by any means) and I thought her bars would come very slowly. She was not super weak, but did struggle with strength. I told her mom she could compete Level 2 this year but bars would be the key event. She worked hard and got all of her skills and I'm so proud.
On the other hand, I have an athlete who has to work so hard on her strength and, in addition, carries a bit of extra wait. She misses practice quite a bit and it seems that no matter how much conditioning we do, she struggles to be strong enough to really progress on bars. I wouldn't let that preclude any child from doing gymnastics, but if it were my child, I would like this kind of candidness just so I could pursue other sports where their body type might be more beneficial.
She's our short stuff.... I am pretty short too (5-3 on a GREAT day 
She is the shortest on her team and in her class.
