A supreme court clerkship is very impressive, but "saved by one of these people" is strong. My understanding is the justices have a conference, stake out their positions, and then the chief assigns cases based on who can attract a majority to their opinion. So Breyer presumably had a rationale that could get at least 4 concurrences in conference. It's possible for the other justices to later change their minds based on the actual opinion the chambers produce, but that doesn't seem to be the case here. It's also possible the case was just assigned based on workload, considering the 6-2 split, almost anyone could have written it.
In other words, the clerks do the work of researching and fleshing out the finished opinion, but I don't think they have much influence on the rationale used to decide the case. I've heard stories of clerks having to write opinions they personally disagreed with.
Breyer was a prominent copyright law scholar before he became a judge. Between that, and the fact that he hasn't gotten many opportunities to write majority opinions in his 27 years on the court, and the fact that he's likely about to retire in a few months, giving him the opinion was the obvious and collegial thing for Roberts to do.
I'm biased, but I don't think the technical elements of this case were challenging to an intelligent layman. I think most people smart enough to become judges can understand the concept of an interface that is independent from an implementation, which is all this case really required, along with quantitative estimates of the amount of code involved. So I doubt that he needed clerks to understand any of it.
While the Supreme Court justice authoring the opinion will have laid out the broad principles and legal framework upon which he/she wishes to make the decision, the law clerks have a central role in crafting the opinion and making sure that the arguments and reasoning are sound.
By the very nature of the court's operations, the justices cannot be writing the 30 page opinion and doing all the research on every case. The clerks are the ones who will be writing most of the summary, determining how certain cases influence the current case, and laying out the draft logic. They'll have many sessions with the justice to test the logic and find edge cases, implications, and make sure that a decision affecting millions of people is sound. Basically debate and draft/redraft the opinion (with other justices + clerks as well) based on what they're finding as the drafting continues.
I would say the clerks are indispensable to the creation of the opinion's outcome.
In other words, the clerks do the work of researching and fleshing out the finished opinion, but I don't think they have much influence on the rationale used to decide the case. I've heard stories of clerks having to write opinions they personally disagreed with.