This is a myth born from many misunderstandings of what in photography is relative, what is absolute and what is perceptually relevant to humans, and also from a desire to believe that there is a magical recipe which gets stunningly clean images.
Having larger pixels does not make photos displayed on screen / paper look cleaner. (Sure, some technologies may not scale beyond a certain threshold.)
Having 1 pixel as large as 2 smaller ones makes no difference (in noise terms)
for the entire image (which is the only thing that matters for a human viewer). What matters is technology and sensor size.
You can read a detailed explanation (with a link to samples) here:
http://www.canonrumors.com/forum/index.php/topic,255.msg3911.html#msg3911
In fact,
http://www.cambridgeincolour.com/tutorials/image-noise-2.htm shows that a higher resolution (= smaller pixels) is perceived as "less noisy".
The explanation is:
"If the two patches above were compared based solely on the magnitude of their fluctuations (as is done in most camera reviews), then the patch on the right would seem to have higher noise. Upon visual inspection, the patch on the right actually appears to be much less noisy than the patch on the left. This is due entirely to the spatial frequency of noise in each patch."
(Search for this explanation and look at the images above it.)
You should also consider that a compact camera sensor is (for simplicity) 16 times smaller that a full frame sensor. This means that one captures 16 times less light, meaning that it's noise should be 4 stops higher than that from a full frame sensor. And it's about there.
What I am saying here is that while a full frame sensor has 10...20 MP, the full frame equivalent resolution of a compact camera sensor is 200...300 MP. Despite this stupefying density, the images from small sensors still have a smilar a noise level for an area with an equivalent physical size cut from the full frame sensor.
Here are even more details:
http://www.josephjamesphotography.com/equivalence/#8
(It's good to read the entire myth section
http://www.josephjamesphotography.com/equivalence/#myths and also the "Noise" section
http://www.josephjamesphotography.com/equivalence/#noise )