I would interpret that as being a case where you effectively get it again as a special case, yes you effectively get the clan basic training 2x but as effectively a different specialty, so lets say you started out as an aerospace pilot, or MechWarrior then you washed out, and trained as vehicle, or infantry. while you likely won't be as good as an infantry (elemental) that trained your whole career but you may also have a better feel for anti-mech tactics, since you started training to run a mech so you have a better understanding of their weaknesses.
I suspect the correct hard rules interpretation is that you would not repeat basic, but instead simply take another advanced field (similar to how if you took 1 basic and then multiple advanced fields in the same module).
That said, I would agree and say it's a special case--you could interpret as the Clans' poor tolerance for failure; making the warrior go through basic again to prove themselves/kind of as a walk of shame. I don't see anything in the Clan Basic fields that likely wouldn't benefit from a second go around, either.
As this isn't directly addressed by the rules, I would suggest this is a good opportunity for GM interpretation to come into play at your preference. For example, you could say that instead of the normal 30 xp + 6 points refunded for each field in the basic, you could have them put 15 into each with no refund (reflecting the limited effectiveness of the repetition).
It's also a good opportunity for some roleplay. Does the character have a large enemy or similar trait, maybe? Perhaps a spiteful superior sets it up where he has to repeat basic. Or high connections? Maybe a benefactor scoots them along in the process.
I'm of the opinion that the module system is best used as a guideline for shaping a character to a certain faction/role rather than letting it define the character. Whichever suits the character or story better (repeating basic or not), handwave it. In the end, the difference is how the player allocates possibly 180 starting XP... pretty insignificant.