Totally disagree with your assertion that being tired is a garbage excuse! And not really sure why you're ranting about the "everyday" guy and how their jobs compare to professional hockey players?! Not to mention bagging on teachers...but oh well.
Anyway, here are some reality based scenarios...
Since the 08-09 season the Hawks core have played 117 PO games, TB has played 48.
In the last 4 years the Hawks have played 71 PO games to TB's 30.
And in the last 3 seasons the Hawks have played 65 to tampa's 30.
Keith, Seabrook, toews, Kane & hammer have all played 100 or more PO games in the last 6 years...that's a full season plus at least 3 PO series. And they're all at PO intensity.
So yeah, they're probably both physically & mentally tired...and rightly so.
Now I'm not saying this is any kind of an excuse (& neither are they, as a matter of fact), but it's reality...like it or not.
As to the oilers and islanders not being tired, I'd bet they were exhausted but I will say this...there is much greater parody in the league today and most of the teams they played in the first round (& some in the second) wouldn't be in the PO's today.