No, he didn't. You can only arrive at that number by ignoring the way the federal sentencing system works, because it's based on taking the maximum penalty for any count of the offense charged and multiplying it by the total number of every count.
In reality, like charges group --- you are typically sentenced based on a single count, usually the most severe of the counts.
Prosecutors threatened Swartz not with 35 years but with 7. But 7 years is an equally ludicrous number for the actual offenses charged, which were non-remunerative, non-destructive, and applied to a first-time defendant. Which may be why prosecutors offered Swartz a plea deal with a custodial sentence just several months long.
Swartz's own lawyer, writing after Swartz's tragic death, believed that Swartz could have gone to trial, lost and been found guilty, and still not served a custodial sentence. Not implausible for a first-time offender who didn't try to make a cent from his offense.
Reporters parrot these numbers because the DOJ supplies them in press releases. DOJ is lying when it makes these outlandish claims, but deception on the part of prosecutors isn't an excuse for reporters not to talk to lawyers before amplifying those lies in the press.
As usual, you can count on Popehat --- a blog run by a former federal prosecutor turned civil rights attorney --- for a pretty excellent summary of how the system actually works:
http://www.popehat.com/2013/02/05/crime-whale-sushi-sentence...
(If you're interested, here's the sentencing guidelines for 18 USC 1030: http://books.google.com/books?id=nZu3w1y4fkYC&pg=PA299&lpg=P...)