So, yeah, bottom line: you only need a delta-V of about 12 km/s to get out of the solar system, but a delta-V of 30 km/s to get to the sun without going into orbit.

This is true, but the possibility of gravity assists mostly nullifies the difference. If you can get out to Jupiter you can basically choose: either let it sling you out of the system, or let it cancel out all your orbital velocity so you fall into the sun.