I think the distinction is sometimes overplayed, but I also think it's a valid one in a certain sense. "Monitoring headphones" can mean various things to different people, but one thing it generally doesn't connote is coloration, warmth, bass emphasis, and euphony. Speaking for myself, I was hoping that the SRH1840 would be Shure's attempt to create something more inline with the latter. I wasn't expecting a D7000 or an LCD-2, but I was hoping they'd stray a bit further from their closed models which are more or less synonymous with "monitoring headphones."
One thing it doesn't have to mean though is harsh upper-end and anemic low-end. There are plenty of monitoring headphones and ear monitors that have a more laid back sound and a perfectly suitable, moderate bass response. The fact that the SRH1840 has a bass response that gets described as less-than-neutral in quantity by listeners is concerning to me, for example.