I think whether you have a hard floor or a soft floor, if they are kept dust free every day then there wont be any issues from either of them. So everyone is right.
In reality though this of course doesn't happen, and so those days that neither of them are vacuumed/cleaned etc then the carpet will 'hold' the particles in place - for longer, as opposed to a hard floor. Just my opinion.
With neglect all surfaces will give an allergy sufferer symptoms , and this can cloud some peoples opinions on whats right and whats wrong for allergy sufferers.
p.s. I have had asthma all my life and feel I speak from experience. I am allergic to dust mite feaces (well the proteases in the feaces I think it is - as opposed to the actual poo).
p.p.s. I'm not taking any sides or being biased, just thought I would post my thoughts thats all. Good debate!