Zapier is a good example of copying a good idea (IFTTT) and fast-following with good execution. Sure, copying can seem lame, but Google was copying Alta Vista, Facebook was copying Friendster, Microsoft was copying everyone, etc.
Good ideas are important but good execution is more important.
It's also unclear just how much IFTTT influenced that start of Zapier. IFTTT was announced only about 10 months earlier than Zapier. Zapier announced right around when IFTTT has a live prototype. REST APIs were really hitting popularity at that point, so services like these were becoming more & more obvious-- simultaneous invention is a thing. [0] Also, years earlier, there had been a relatively similar offering from Yahoo, Yahoo Pipes, [1] so the idea was pretty much out there before both of these companies. The rise of REST APIs really just made it much more feasible.
We can't run the experiment but it's safe to assume most startups that took very early funding did need it to succeed. That doesn't really take away from the founders effort though. Although it does mean there were probably 10 other teams that had the same idea and skills that failed for not having the ability to raise funding.
Good ideas are important but good execution is more important.