Memory typically runs at 1.5V, so to use 15W per 1GB, a 4GB DIMM would be pulling 40 amps. There is no way that much current is going to be flowing through those tiny traces on a motherboard.
http://www.valueram.com/datasheets/KHX1600C9D3_4G.pdf
According to this datasheet, that 4GB DIMM uses 1.41W, which seems substantially more believable and realistic. That may be at 1.65V rather than 1.5V, but either way, we're talking about a very tiny amount of power compared to a video card or proc.