Mine is the large plastic pitcher (I travel with it as well when I go to NJH or anywhere else and it survives the flight LOL) and I leave it on the counter because I only use it to rinse vegetables, fruits, coffee, etc. I drink Poland Spring bottled water since it has been tested and highly approved by Dr. Falkinham to have little to no NTM.

I used to leave my glass LifeStraw pitcher on my kitchen counter until I noticed a green tinge to the water. I researched and found this : "Even the purest water is rarely free of living organisms or microbes. By placing your water bottle in an area that's well lit, these living organisms will start growing. The growth is what begins to make the bottle to begin turning green." I gave it a thorough cleaning and now always keep it in the fridge. I am guessing, if you prefer leaving it on the counter to do what sadair does, to only filter water that is needed at a time.
I do like the LifeStraw, use it exclusively and hope it is doing what it is supposed to in terms of killing 99% of bacteria.