^^
Not true. I am not sure where you heard this but there are soooooo many rumors about why puffers puff.
They do often tend to inflate in captivity for little to no reason but thats not to say its stress free. Puffing puts so much strain on their body and does not feel good. Most likely he is indeed scared of something or was startled. Thats not to say its horrible but it does stress them.
Inflating is a defense mechanism and can decrease a puffers immune system and life span. It puts a great deal of pressure on their internal organs. They don't actually "puff" up per say, they actually pump water into their stomach which expands to nearly a hundred times its original volume. This is possible because the puffers stomach is pleated, like a skirt. They have so many pleats in their stomach that you need a microscope to see the smallest ones.
As the puffer fills with water its spine bends into an upside-down U and the liver, intestines, and other internal organs get very tightly squeezed between the fish's backbone and its now huge stomach.
They have two layers of skin too. The outer layer is elastic and stretches when they inflate. The inner layer is fibrous and actually pleated like the stomach. So if they did not have the outer 'stretchy' layer, they would look hilarious (all wrinkled up) once they deflated
The outer layer of skin also works to raise the spines of the puffer up...
Another interesting fact about puffers is that their stomachs have lost all digestive function.
A few biologist actually believe Puffers have evolved from Triggerfish who can do the same 'pumping' of water with their stomachs. But if you watch triggers do it, they simply pump water in a bit (not to the stomach) and then blow it right back out to move sand around and flip urchins over. But its the same action.
Anyways, a bunch of random stuff here but the bottom line is that they do not have 'fun' puffing up and its certainly NOT stretching.
You say try keeping your arms at your side for a few weeks and then see if you want to stretch--try this instead. You feel normal and loose but then you suddenly get startled and react by filling with air like a balloon as your internal organs squish up into a fraction of the area they usually occupy and press against your spine which is now also bending with great strain...I bet you will like to deflate as quick as possible and never want to inflate again
They are not stiff and need to stretch. In fact, after inflating I bet they do not feel too well. There is just so much pressure put on their body when inflated. Their skin stretches so much that the collagen fibers are stressed directly and the skin becomes stiff.