It's different pitch, but a natural and logical progression. Most of the time ideas need refining, especially with user feedback. It doesn't make sense to start with a new company since the technology that powers is still the same.
If you're changing everything, then it makes sense to just start a new company.
So I guess it can be a judgment call. In your case it sounds like you're doing the right thing, though.
"...that 25k he just gave you, could've gone to his kids' college fund or investing in blue chip stocks instead. It's amazing that you can raise money at all."
Angels give less money than VCs, some angels give low amounts (15-25k) especially in an early seed round. They're doing it for you. Screwing them over for more equity or YC makes you a shitty irresponsible human being and imho, should be considered a type of fraud.
Honestly I'm surprised at Sam's stance. Unless it's really justifiable, this seems like bad advice.
Of course, that's a completely different scenario from simply evolving the idea in a different direction but still keeping the core; in that case, I agree with your point of view. For example, I do see a problem if you're going from a "Custom CNC Furniture" idea to a "Custom CNC Cycling Parts" idea. It would be pretty shady to screw over your initial investors in that scenario. It also might be actionable by the original investors if you reuse any assets you developed using their funds.
Your point is well taken, though. I wonder if there might not be a middle ground, where a new company is formed with the old company owning some of its stock. This gives the new venture a cleaner cap table while not completely screwing the original investors.