Corruption is something a government can have; what does it mean for a party to be corrupt?
If people think it means the party doesn't reflect the will of the voters... Not exactly. That's always been the structure of the Democratic party. Popular will is tempered by party leadership. That's baked into the structure of the Democratic party itself. The party that lacks that kind of tempering is the GOP, and as a result it tends to run populists who may or may not actually have any government qualification (one won the Presidency in 2016; a couple have won state governorship over the years).
The resulting apologies and resignations were an attempt to reconcile with voters who, fundamentally, did not understand how the party they support actually works. No shame in that; it's a big and complex machine. But it's never been a machine that just reflects the unmodified will of the people who toss ballots into the box with a 'D' next to their name in the primaries. That's one source of signal the party uses to decide who it will run.
To give another example: in 2008, in response to the Florida party leadership running their primary earlier than the national committee authorized them to run it, the committee stripped all the Florida delegates of their vote in the national convention (https://en.wikipedia.org/wiki/2008_Florida_Democratic_presid...). Then, it compromised (at its discretion) by seating them but only counting half of each of their votes. That is the nature of the power the democratic party national leadership has to wield at its discretion, without oversight, as per its charter.
People just don't know this because people don't know the parties.