I have some issue with my stomach where the opening at the top (I don't know the English word for it) won't close properly, regularly giving me acid reflux. Very annoying... went to see a doctor about it, he stuck a camera on a stick in my throat to look around and told me this.
He then told me not to consume (much) of the following:
- fat
- alcohol
- acid (like in Dr. Pepper :'()
- sugar
- spicy food
- caffeine
- pretty much anything else that's worth enjoying you can think of
I think the reason was that when you consume these things, your stomach will make more acid to deal with it. So yes, spicy food itself doesn't hurt your stomach but you might feel heartburn or acid reflux.
As mfatal said, moderation is key :-)