A request for evidence of the US visa means you've fewer document requirements than those from your country without this, all else equal, so it helps but it only helps at the margin.
My wife was refused a TRV when we were just dating for the unstated reason that there was a romantic interest (they hint at it with "purpose of visit") despite the fact she had been to the US. They checked off "travel history" as a reason for refusal despite the trip to Florida.
As the immigration lawyer Peter Rekai told a parliamentary committee, do not put too much faith in the so-called reasons for refusal:
"What we do have to get away from is an officer's belief that he or she must take the form that refuses an application and arbitrarily X a number of the boxes that indicate specific reasons for the refusal, reasons that may not—and likely are not—the actual reasons for the refusal. Worst of all—and this happens all the time—officers feel compelled to check the box saying that neither the applicant nor the host has shown sufficient financial means. Typically, a 50-year-old, well-established Canadian client will come to me and say, “My nephew was refused. We've provided all kinds of financial information, but I'm going to go to my accountant and my financial adviser and we're going to present all this information back to the visa office.” I say, “No, that's not the reason he was refused. Your nephew is 22 years old, he is unemployed, he is single, and he is from Iran. Nineteen out of 20 of those applications are going to be refused. Save yourself the trouble, save your MP the trouble, and save the visa office the trouble of the second application where you pursue an avenue that has nothing to do with it.” These types of arbitrary check-offs—and they're done all the time—lead to an enormous amount of work and are basically a waste of resources. Typically, the second application comes back with different boxes checked for the refusal."
