But I've heard that the quality of the recorder device has no effect over that when picking up the soundboard feed, no matter how good it is. Is that true?
Generally speaking this is wrong, but the difference is less using line in than relying on mics+mic in.
The onboard components on your recorder
do matter, especially the A/D converter. Since you have to convert the analog SB feed to digital, you need to go for a unit with a good A/D.
I agree with the R09/R09-HR recommendation. It's an ideal upgrade path too, if you want to add mics later on.
If you don't mind carrying around more gear, an alternative would be UA5 (digimod, $120 or so on ebay) > used MT or MT II as a bit bucket (I think I've seen them around $200). Add a few bucks for powering and cables though. IIRC you're restricted to 24/48 though, but that should be sufficient for you.
But maybe most people here would still say that you'd get better sound with the R09(-HR), than with the UA5>MT combo... Opinions?!