I had a big post that got deleted because I was logged out, but Miami's 3P performance in the play-in plus the playoffs was very feast or famine. They were about average in the play-in, caught fire against Milwaukee, struggled against New York, caught fire again against Boston, and came back to earth against Denver:
(Column is overall FG%, green line is regular season FG%, yellow line is regular 3P% and black line is 'playoff' 3P%)

Whether it's terrible shooting luck or not, I'm not sure anyone could look at the tape to find significant differences in how to defend Miami from deep between the ways Milwaukee, New York, Boston, and Denever looked to play against Miami.
Always possible I copied a row wrong, of course, but I don't think so. Data is from BBRef.
One last way to think about Miami's shooting to put it to bed (chart for visual aid): out of all the teams Miami played in the postseason, who allowed the fewest wide-open threes on their way to the Finals?
A: Boston. It didn't matter.
The numbers:
The Heat averaged 11.0 wide-open 3s per game.
14.2 Open 3's and 14.2 Wide-Open 3s against the Knicks,
16.4 Open 3's and 10.4 WO3 against the Bucks,
13.6 Open 3's and 9.6 WO3 against the Celtics.
Or, for what we really care about (New York vs. Boston):
The Heat shot 31.8% on open 3s and 37.6% on wide-open 3s against the Knicks.
Against the Celtics these numbers were 42.1% and 58.2%.
I've been up for a while, so my numbers might be off, but the upshot is that Miami made something like 15% more open- and wide-open threes against us compared to their shooting against New York even though they were getting... 19% fewer of those looks in total? (23.2/28.4)
In the words of the best Steven A Smith parody on the internet: "To me, that's preposterous. Crab Rangoon, things of that nature."