Human-rating the then-new Falcon 9 launch vehicle was part of SpaceX’s award for Commercial Crew starting in 2011, and the launch vehicle did not delay the program, so I think it counts. Falcon 9 had flown twice when NASA made the initial award, it certainly wasn’t a proven launch vehicle and it’s easy to imagine it tanking the whole program if it went differently.
Flown twice is still pre-existing---the vehicle had been in development years before the award. If your point is that the Falcon was pre-existing and it still took a long time to get to crewed flight, that's true. But note that the adage doesn't say the launch vehicle is the only source of delay, only that it is generally the most significant one.
A better counterexample would be a crewed program that developed its own launch vehicle and still completed on time and within budget. If you treat the Falcon 9's development time as part of the overall project (which you should if you're maintaining it's a new vehicle per the adage), then you're looking at something like 15 years just to get a crew to orbit. Which is consistent with the rule.
Yep, they didn't develop a new booster or stage 2 for Crew Dragon. No new launch vehicle.
Starship is likely to be similar. Super-Heavy (the launch portion of the combined vehicle) isn't likely to be scrapped for the crew version after the cargo Starship is ready.