Nash and Paul's style of play are not the type of ball dominant players that you should want to play for your offensive system for the simple reason that they both led their team no farther than the playoffs.
However, the styles of Jason Kidd, Gary Payton, John Stockton, Terry Porter, Kevin Johnson, and many other "true PGs" have made it to the finals, and some won rings. And the year Iverson led the pathetic East into the playoffs, he wasn't the leader for assists for his team. In fact, he wasn't even in second place, he ranked 3rd behind McKie and Snow. One might argue that he was playing combo guard, if not SG. And they went 1-4 in the finals, which was only surprising in that most people expected them to be swept.
Here's a list of the NBA finalists for the last 20 years, with the name(s) of their assist leader(s) for those years - where there is no clear leader, I may list multiple players who are close to the top, starting with the assist leader and working down. Over half the time (11/20), the winners were playing the Triangle, and the nominal PG was a fairly insignificant role player. In most of the remaining cases, the PG was either an actual PG, or the real PG was someone playing out of position. Out of 40 finalists, in only 4 cases (Detroit, Isiah Thomas, '90/Seattle, Gary Payton, '96/San Antonio, Kidd, '02/NJ, Kidd, '03) was the PG both the assist leader and leading scorer, and in those the player in question was generally considered a true PG despite that.
Here it is, make of it what you will:
1990: POR vs
DET: Terry Porter vs Isiah Thomas
1991: LAL vs
CHI: Magic Johnson vs Scottie Pippen/MJ
1992: POR vs
CHI: Terry Porter/CDrexler vs Scottie/MJ
1993: PHO vs
CHI: KJohnson/CBarkley/DMajerle vs Scottie/MJ
1994:
HOU vs NYK: Vernon Maxwell/Kenny Smith vs Greg Anthony/John Starks
1995:
HOU vs ORL: Sam Cassell/Kenny Smith vs Penny Hardaway/Brian Shaw
1996: SEA vs
CHI: Gary Payton vs Scottie/MJ
1997: UTA vs
CHI: John Stockton vs Scottie/MJ
1998: UTA vs
CHI: John Stockton vs Scottie/MJ
1999:
SAS vs NYK: Avery Johnson vs Charlie Ward
2000:
LAL vs IND: Kobe/Shaq/RHarper/DFisher vs Mark Jackson
2001:
LAL vs PHI: Kobe/Shaq/Fox/Shaw vs McKie/Snow/Iverson
2002:
LAL vs NJN: Kobe/Fox/Horry vs Kidd
2003:
SAS vs NJN: TParker/TDuncan vs Kidd
2004: LAL vs
DET: GPayton/Kobe vs CBillups
2005:
SAS vs DET: Parker/Ginobili vs Billups/RHamilton
2006: DAL vs
MIA: Terry/Nowitzki vs DWade/JWill/GPayton
2007:
SAS vs CLE: TParker/TDuncan/Ginobili vs LBJ/ESnow/LHughes
2008: LAL vs
BOS: Kobe/Odom/Fisher/Farmar vs Rondo/Pierce
2009:
LAL vs ORL: Kobe/Gasol/Fisher/Odom vs Turkoglu
2010:
LAL vs BOS: Kobe/Odom/Artest/Gasol/Fisher vs Rondo