Well, they’re both wrong. If you have a permit to own a particular type of weapon, you can buy the ammunition. Military rifles are a weird category of their own. Up until fairly recently, you were given a sealed, 50-round box of ammo for your service rifle, so that you could respond quickly if the militia was called up. That’s been discontinued. But you can still quite legally buy ammunition for your service rifle as long as you have permits for that type of firearm otherwise. (This is based on what I can find and read regarding gun regulation in Switzerland, although some of this may have changed since the EU imposed new restrictions on member states.)
There is some variance in application of gun laws, as many of the permits are ‘may issue’ rather than ‘shall issue’.
I could be wrong. I would suggest consulting with someone that specializes in Swiss firearms law, as some writeups are giving contradictory answers.
Regardless: Swiss gun ownership is estimated to be among the highest in the world, with the US being highest by far. Despite their very high rates of gun ownership, they also have a very, very low homicide rate in general, and their rate of gun crime is microscopic.