Right, but I'm going to guess that even though it's fine if Randolph and Cary went together, chances are that they didn't because those most likely represent School, Sport or Club rings more than anything because when we were discussing this on Randolph's board, someone suggests that these are not romantic rings because her grandfather wore one.
In the 1950s and 1960s, these rings became a self-identifying symbol in the gay community, worn by both gay men and lesbians. 
A pinky ring did not have a set significance in the way that a wedding ring does. They were used by different people for different purposes including, I am sure, decoration.
As far as I can tell, the two rings are not identical. Cary Grant's seems much thinner, but I don't believe that matters at all.
That's enough proof right there to indicate that these two were only great friends and roommates
I cannot believe that you are actually arguing that if pinky rings did not always
indicate gays, then the fact that they were wearing pinky rings is conclusive proof that they weren't gay. That does not even begin to make sense.
I take it you do not have even a cursory knowledge of Cary Grant's marriages. #1, #2 and #4 were "poor, nasty, brutish, and short." Grant admitted in an interview that his first two wives accused him of being homosexual. Marriage #3, Betsy Drake, was "poor, nasty, brutish, and on paper, longer." According to an interview with her included as an extra on one of Cary Grant's films, the marriage as a marriage did not last very long, but it was quite a while before they got a divorce. Marriage #5 was when Cary Grant was something like 77.
It would be rather implausible to get the idea that those two would wear each other's together rings on film after going though all of that trouble to keep denying rumoros
As I said, pinky rings did not have a set significance and so they could be used as an in group joke that was quite deniable. If, in 1940, the "gay" significance of pinky rings was confined to Hollywood or to communities of actors, there was little risk of exposure. The usage seems to have only become widespread later on.
This movie was made in the middle of the "Beach House" period. To anyone in Hollywood, the whole movie is an in group joke if only because of the rumors. Two men who are linked romantically competing over a woman is funny whether the rumors are true or not. But certainly funnier if they are true.
P. S. When a few years earlier, Cary grant famously said, "because I just went gay," the censors had no problem with it because the usage that he was referring to was confined to homosexual communities and their friends. They were the only ones who got the joke.
Grand was not saying, by the way, that he just became a homosexual. Gay was not used as a general term for homosexuals at the time. He was saying that he just became a fairy, a subgroup of extremely obvious and effeminate gay men, when he was asked why he was wearing women's clothing. He then jumps and flounces his arms, a stereotype.