But after doing some research, you are right! Dry sugar will not hold onto any types of bacteria or anything like that.
You are not wrong. Sugar is NOT an antibiotic in any way, shape or form. Bacteria do require an aqueous environment (water) that is within their tolerance in order to thrive and reproduce. They can survive dried out for some time, or at least their spores can, as can wild yeast.
So, here's why things don't rot:
SUGAR - dry, won't rot unless it gets wet
STALE BREAD - dry, can mold, but won't rot
JELLY/JAM - too sugary, osmotic pressure will kill any bacteria trying to live there
(caveat: jam & jelly can rot on the surface if a drop of water drips on it)
SALT WATER - osmotic pressure again
KOOL-AID - will spoil if not over-sugared
SODA - most have preservatives, low pH also protects
LEMONADE - low pH, also often has preservatives
COFFEE - if milk and sugar are added, will rot, otherwise, no food/fermentables
WINE - alcohol levels generally high enough to protect it
BEER - can definitely spoil/rot if certain microbes get into it
So, I would most HEARTILY recommend boiling your sugar before putting it in beer.