Difference of opinion: Take a look at both actors/actresses in the 2000's:
Best Actor in the 2000's
2000 Russell Crowe - Gladiator as Maximus
2001 Denzel Washington - Training Day as Alonzo Harris
2002 Adrien Brody - The Pianist as Wladyslaw Szpilman
2003 Sean Penn - Mystic River as Jimmy Markum
2004 Jamie Foxx - Ray as Ray Charles
2005 Philip Seymour Hoffman - Capote as Truman Capote
2006 Forest Whitaker - The Last King of Scotland as Idi Amin
2007 Daniel Day-Lewis - There Will Be Blood as Daniel Plainview
Best Actress in the 2000's
2000 Julia Roberts - Erin Brockovich as Erin Brockovich
2001 Halle Berry - Monster's Ball as Leticia Musgrove
2002 Nicole Kidman - The Hours as Virginia Woolf
*2003 Charlize Theron - Monster as Aileen
*2004 Hilary Swank - Million Dollar Baby as Maggie Fitzgerald
2005 Reese Witherspoon - Walk the Line as June Carter
2006 Helen Mirren - The Queen as The Queen
2007 Marion Cotillard - La Vie en Rose as Edith Piaf
I'll give you 2003 & 2004. I might give you Nicole Kidman for wearing a prosthetic nose.
And hey, if having a death scene and a troubled life counts, well, I'd include Cotillard. Otherwise, I'm having trouble coming up with an amazing number of Oscar-winning actresses from 1980 - 1999 that fit the hypothesis, at least for the course of a movie.
Of course, I'll defer to Shammrog about his former avatar's TWO Oscars for best actress.
Swank's performance in MDB was great.
On the actor side, I agree with your hypothesis during the 1984-1996 stretch (F. Murray Abraham, Cage, Hanks, Hanks, Dustin Hoffman, Hopkins, Pacino, Geoffrey Rush).
Other than that, I don't think the hypothesis is as amazing as you stated, especially in the 2000's.
Cheers,
Lavabe