Okay, this secret is IMO very clumsily worded, but from what I understand, OP is claiming that James, Sirius and Peter were the three ‘real’ (ie close) friends, at the expense of Remus who was the tagalong that they didn’t really like or trust as much as the three ‘human’ Marauders.

First of all, I’m a bit annoyed that the one Marauder who the OP excludes from the friendship is the werewolf, the non-pureblood. I don’t like the notion that he was James, Sirius and Peter’s charity-case friend, the one they included not because they liked him but because they felt sorry for him. Nobody voluntarily takes on an ADVANCED, DANGEROUS AND ILLEGAL branch of magic that takes you three years to master in order to be there for their ill friend’s ‘episodes’ which make him VIOLENT AND UNPREDICTABLE for someone they don’t like, trust or respect much. No, really. You might pat them on the head afterwards and buy them some get-well chocolate, but no Animagery unless you genuinely love them to pieces. 

Second, if this secret specifically refers to the post-Hogwarts period of MWPP, especially in 1980-1981 during the war, then if I tilt my head and squint it can be argued as being somewhat true, especially if Peter was encouraging them to doubt Remus - which he probably was, to cover his own tracks. Remus’ lycanthropy, the way he would be treated by society and his spy work for Dumbledore among other werewolf packs would have given Peter solid ground to work with on making Sirius doubt him. Because Sirius is the only one of Remus’ close friends explicitly confirmed to have doubted him, with Remus stating that James would have considered it unforgivable to mistrust a friend and Dumbledore (who is also a trusting, second-chances kind of man) would have known that Remus was spying for him. Presumably other members of the first Order mistrusted him as well, but not all the people who were important to Remus.

The whole point of the Marauders is four extremely close friends who were practically brothers of the heart where they loved each other enough for three to band together and take a huge amount of risky effort to make helping the fourth to manage his painful and stigmatised medical condition a large part of their lives. Which made the later betrayal all the worse. 

On a side note, I used to use the phrase ‘true Marauders’, but now that I consider the risks that Peter took for Remus (and let’s face it, come full moon Moony could swallow Wormtail in one gulp!), I prefer the term ‘three loyal Marauders’. Peter was a true Marauder, he just failed to stay loyal to the other three.