That smells like bullsh*t to me.
LSAT/MCAT scores are averaged by virtually all schools, but then again LSAT/MCAT averages are generally higher (ie Ivy Law schools' scores average 99th percentile), so they can be a bit more picky.
In regards to GMAT, from my experience, the highest score is almost always taken. It makes sense-- schools are based on their rankings, which are heavily influenced by their average GMAT scores, and being ranked high equals more applications which equals more $$$$$$, which is what bschool is all about,
I'm a professional GMAT tutor, and I've seen about 40-50 people be admitted, and virtually all have written the GMAT multiple times (one girl wrote it 7 times I believe). She got into her school of choice, wasn't even asked about it once.
IMO let's just say this-- it's better to write it 5 times and get a 690 somewhere there in than to write it once and get a 590.