I think it mostly has to do with the OG of your wort. If there are enough yeast cells to ferment the beer, without the need to reproduce, then oxygen may not be required. BUT if the yeast do, in fact, need to multiply, then oxygen is most definitely needed. Which would support the idea of needing to oxygenate high gravity wort, but not low gravity wort.
The best idea is to just use Mr. Malty and figure out exactly how many yeast cells your wort needs and make your decision based on that. A 1.048 gravity ale, fermeted with dry yeast with 90% viability, requires 177 billion cells, which is a little less than a 11.5g packet of dry yeast(~200 billion). In that situation, pitching the entire packet, you would not need to oxygenate.