Looking over Ascent's graph of the ride, i see the following notable climbs:

sea level to 666' (in 1.8 miles from my door, damn it!)
429' to 529'
478' to 610'
303' to 610'
428' to 518'
414' to 666'

That totals to about 1550', without including any elevation change lower than a 90' swing, and of course there are dozens of those on this kind of terrain. Adding in the major ones of those will get up to the 2000' numbers and then I suspect with the "correction enabled", they are including every single little change in elevation and that's why it's even 800' higher.

(This is basically the usual way out of town for me. I live at the beach and am surrounded by 700' to 1000' hills so first thing off the bat I have to climb. But I get to finish the ride with "the reward": from 666' back to sea level in a curvy 1.8 miles at 40mph+! Yippy!)