Moses and Joshua, a legendary duo to say the least. These were two men that shared many miracles and had many different miracles separate from one another, one where they had a relationship based on quite a few things, but as we see in Exodus chapter 17, we realize that this relationship was built on the trust of each other's abilities. This is why the only other person who went up the mountain to visit with the Lord was Joshua, Moses' assistant. (Exodus 24:13) While these two men didn't grow up together as Moses and Aaron had, Joshua and Moses, I think, grew the most together. These two men had shared a common interest, fought the same battle, and served the same Lord with a very similar fervor, and zeal.
I am very much intrigued by the parallels of their ministries, and I think it's worth a study for a later time. Yet it's fairly easy to see echoes of Moses' life and his victories in the life of Joshua, his closest follower and "assistant", which interestingly has a facet of the word 'ministering' that may be worth another blog post to uncover. I don't necessarily believe that Joshua's ministry unto Moses was what legitimized their relationship, but that they had a common goal, and a very similar birthright. They were designed to liberate the Hebrew people, to bring them to a closer place of worshipping the Lord, and to take the land that the Lord had in mind when He created them. They were to perform miracles and outstanding deeds by faith and by the power in the Lord.
Yet I think the marking factor of the legitimacy was that they went into the presence of the Lord together. Joshua went up with Moses, and suddenly, I think, everything he was doing up until that point and everything after that point had made sense to Joshua. There was an imprint, kind of like when you close your eyes and flash a flashlight in your face, you see an imprint of the "glory of the flashlight". This was when Joshua's ministry changed from ministering to Moses to ministering to the LORD GOD. This was their common goal, and them coming into the presence of the Lord was the one mark that they both had in common which began the journey of their mutual respect and love for one another.
Sure you can boil it down to just the fact that they did ministry together, and a similar type of ministry. You can even language it in such a way that they found intimacy with one another in their work, but when you go and stand in the presence and gaze of the Almighty God it's difficult to boil it down to just that. They ministered unto the LORD, they had experienced this profound holiness that had marked their lives and their relationship for the rest of both of their lives. I think the legitimacy was found in how much they welcome the presence of God into both of their lives and had found a common love for their God.