First, it needs to be remembered that in each hunt, the Master(s) is/are the Final Word on attire. If a hunt says that members with colors wear pink coats and purple boots, then that’s what’s correct for that hunt.
That said, the rule for black boots with brown tops is those are the correct boots when one is wearing white breeches. And the garter straps need to be white to match the breeches. As has been noted, it is universally correct (I’m aware that some MFHs might not be up on history and tradition) for gentlemen without colors to wear white breeches with a black frock coat. In which case, they’d be needing brown tops on their boots.
Contrary to what one might be led to believe by reading some posts here, it is also perfectly correct for gentlemen with colors to wear a bowler, black formal three button hunting coat, buff or canary breeches, and PLAIN BLACK BOOTS (again, boots with brown tops ONLY go with white breeches). In some hunts, only staff wears scarlet, no scarlet is worn by field members.
So, in summary, the boots are not earned. Colors and/or buttons are earned. If those colors and/or buttons are worn with either a frock coat or a scarlet coat, then white breeches are required. If white breeches are required, then boots with brown tops are required.
And, as has been noted, beginning decades ago, the evolution of brown tops in the show jumping and eventing world took its own path, with the attire tradition of scarlet coats and white breeches to represent one’s country requiring brown tops (because white breeches are being worn).