"So .. first - is that true? Second, does it matter?"

To the best of my knowledge, no, it's not. All sorts of people, including pipers & drummers, wear plaids of varying descriptions; there's even an Irish plaid called a brat. The only restraints I know of are the display of heraldic arms to which you're not entitled, and the wearing of eagle feathers in your bonnet (these aren't just traditional conventions, but actually Scottish law).

"What is the proper place to wear a plaid *today*?"

The Prince Charlie is formal attire; so's the fly plaid. If you attend a formal event (St. Andrew's Dinner, Burns Night, regimental mess/mess night/dining in), or an event where the invitation specifies "black tie" or "formal wear", you can wear your plaid, pinned to your left shoulder beneath the epaulette, upper edge of the brooch even with the top of your shoulder and emblem displayed on an even keel; not cock-eyed. The plaid should fall to about 8" or so of the floor behind you.

Dealing with mother-in-laws, now that's another kettle of fish entirely...