Tricky. I am always leaning towards having the movement looked at (at least) by a watchmaker in order to actually adress possible need for service. I have a very good watchmaker here in NY that specializes on vintage pieces, he is my normal first stop. If the piece needs authentication (yours doesn't seem to) I may take it to Aaron Faber to get it looked at and authenticated. Aaron Faber charges about 100 for authentication, my guy takes a look at it for free (but I buy him lunch) of course if service is needed then he changes accordingly.
I recently bought and brought in for service a De Luca 1st Gen. The grand dad to the Rainbow model. He went through his motions, opened it, took a deep look and tinkered a little and as luck will have it he said it had been serviced within the last year or two. And then gave me the overall assessment on condition, bracelet, etc etc
I also brought a GMT Pepsi from 1969 and he had a very similar response to the Torneau guy. He said the movement looked, understandably, a little worn, but that he did not recommend servicing as long as it was keeping time and functioning to spec. He did say if I wanted he can take it and service it and take my money, but that it was not needed on this watch.
I talked to him about preventive and he agreed it is necessary to look at watches periodically, but if nothing was identified a full service would not prevent an old part from breaking, and if you're just going to replace everything that could break you may as well just wait until it breaks. He is a very very experienced Russian watchmaker and has serviced many watches for me and my wife and friends so I trust him.
"I am like a doctor" He said, "If you're sick I fix you,If you're not sick I can give you vitamins and recommend you some exercise but that won't keep you from being sick one day" then I told him about the oil and he said both watches where oiled appropiately and the oil was not going to be a problem..."But that's why you have to take a look at them. too many people will want you to service because they want your money, I have enough work as it is so I don't need to do that"
What I would NOT do is not service a watch that no one has taken a look into. Nobody can tell what is inside without opening it. In the opposite side of the spectrum I took an IWC for service that was running well and when opened it needed some very important work because I had smashed it and everything was out of whack...how it was still working is a credit to the brand, but a 500 service saved a 5000 watch.
So, OPEN IT