A stupid thing that’s never really explained to you is that for some reason for like 90% of the automated sections as long as you don’t put a single input into your controller it will work.
The thing with Sonic Heroes is control sensitivity. What killed you here wasn't the Rocket Accel, but somehow Sonic reading a left input.
Much like SA1 and 2, Heroes reads raw inputs. So even if you think you didn't touch the stick, Sonic will actually move at a hairpin nudge.