If the fitting and the rivets are not loose I wouldn't touch it. It has likely been that way for 37 years. Do keep an eye on it for signs of the rivets loosening. You have good baseline pictures of what it looks like today, compare them to how it looks a month from now and a year from now.
If it is really bothering you, go ahead and drill them out and put new ones in. It's not that difficult. Just make sure you use equivalent rivets. They appear to be all stainless (body and pin). Also use a proper bedding compound like Tef-Gel.