Hmm.. Can it go both ways?
No. Single malt whisky isn't fortified.
And there is nothing wrong with putting Scotch thats less than 60 bucks a bottle over ice
Yes there is.
Lowering the temperature of the whisky reduces the efficacy of the volatile aromatics which deliver the olfactory experience that comes with good whisky.
Furthermore very cold liquid, which alcohol (antifreeze) quickly becomes when ice is added, numbs the palate.
or even adding a little water
Adding a small quantity of still spring water, not chilled of course, does benefit some whiskys.