Well, IMHO, I'd hesitate to use the phrase "extremely important" in anything involving this issue; in the grand scheme of things I personally feel that this whole sample rate issue is towards the bottom of a long, multi-page list of things that really matter when it comes to making a good-sounding recording. This is a huge mountain made out of a tiny molehill of a variable, IMHO.
That said, when it comes to gear, everything comes down to signal chain, and every link in that chain has to be considered in the overall equation. If link A increases quality by 10% (I'm using very generic terms and numbers here just for illustration, don't take them as factual values) but link B decreases quality by 10%, it doesn't make a whole lot of sense to have both of those links in the chain (unless there's a desired color change involved.)
So, yeah, in that respect, SRC quality is important, yes. *If* one happens to have a converter that does indeed seem to sound better at a higher sample rate for whatever reason, but the down conversion for whatever reason largely negates that advantage, then it's just one step forward and one step back, and one has wasted their time/energy/resources for nothing.
Funny how Carl Perkins, Frank Sinatra, Elvis Presley, Bruce Springsteen or U2 never seemed to lose any sleep over any of this stuff though...
G.