We have carpet over concrete and rainy season (and a few
  overflowed tubs and one ... Backed of septic system ... I've
  seen said issue. Indeed it is mystifying. I have a possible
  answer that comes with corresponding emotion of true/this is
  fact. Ignore carpet. You have water on the concrete. Huge
  puddles. Carpet only shows initial boot print at first but the
  puddle of water was already present in other nearby areas under
  the carpet - only revealed later. Fibers in carpet and towel
  alike hold surprisingly less water than a concrete floor can.
  Corn starch holds more, but may be too messy for cleanup.
  Unfinished concrete is also an excellent sponge with many tiny
  hiding holes for water. Porous. Caves. Carpet has caves too but
  not as many. Also if you have carpet padding underneath...
  That's a SPONGE of HUGE surface area. Yet ... I believe most of
  the water was on the concrete itself. Passed through quickly but
  was slower on it's return back up to the surface where you can
  see it and a towel could pick perhaps a 1/2 cup of water at a
  time off of. I measured a few years ago. (Found flax seed a
  perfect temporary damn maker for broken AC drip tray - glutinous
  but amazing. I experimented with many things to soak up/ contain
  water.. Many surprises. Corn starch also a winner. Messy too.
  But this was on concrete/painted latex. Different scenario
  altogether. Water on a balloon vs water on a really hard sponge.
  (Unfin conc). Thus ends brain dump. Thoughts welcomed. Humans
  are lucky with our silicon skin producing silicon oils. Makes us
  nice and waterproof. Poor concrete gets soaked. Even latex
  (rubber/paint/a balloon stretched over surfaces) isn't as good
  as our silicon skin. That's why we wash up so easily. Paint
  doesn't stick to silicon caulking but it does to concrete, which
  is fluffy. Interesting to note: Portland cement is made by
  hydration. It hardens when wet.
  http://www.cement.org/cement-concrete-basics/working-with-concrete/curing
  here is. Cement must stay wet to cure. I wonder if it is ever
  cured of it's thirst of water.

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