My take on the "Remington trigger issue" is and has always been that there is occasionally a problem with these triggers firing when the safety is released. This happens when the trigger is pulled with the safety engaged and it happens on individual triggers in which the parts are dimensionally flawed. In other words, the presence of the trigger connector (or not) has nothing to do with it. I have debated this with Jack Belk before and we simply disagree. He chooses to blame the trigger connector though there is no concrete evidence that it is indeed, at fault.
Like Malm and unlike many of those who post opinions on the issue, I have adjusted, removed and replaced, modified, and serviced, hundreds of these triggers. I have what I must, blushingly, aver to be a superb understanding of the function and design of the "Walker" trigger.
What Mr. Belk espouses is an opinion; nothing more or less. In truth, my contention is the same; it is my opinion. Like that of Mr. Belk, my opinion is backed by years of hands-on experience and a good understanding of mechanical design and function. In the end, you pick the opinion you like and run with it.
Regarding the rifle in the original post, a trip to a competent gunsmith will undoubtedly, as Malm stated, cure the problem. Neglect or maladjustment by an incompetent workman will cause the problem to return. GD