After some research, I believe the answer to be that there are 3 different people who answer to achieving the most premierships as VFL-AFL players and coaches:
The first was Jock McHale, who won 2 premierships solely as a player for Collingwood - the first being in 1903 - his first year at the club. He then went on to coach Collingwood to a record 8 premierships = 10 total premierhips.
The second was Norm Smith, who played for Melbourne Football Club from 1937. He played in 4 premierships for the club. Later he went on to coach 6 premierships over an 11 year period = 10 total premierhips.
The third was Ron Barassi, who played for Melbourne, winning 6 Premierhips as a player only with that club. Following his time at Melbourne, he accepted a coaching opportunity with Carlton, which club won 2 premierships during his short stay with the club. He then went on to coach North Melbourne for a further 2 premierships = 10 total premierships!
However, of those premierhips, some won by Ron Barassi and Jock McHale were achieved as playing coaches.
Essendon and Carlton have both won 16 premierships - the most premierships won by any team. Hmmmmmmmmmmm that`s interesting about that.
As a player only, the record is held by Michael Tuck - 7 premierships.
Carlton and Essendon have 16 premiership's each. Collingwood has won 15.
Essendon and Carlton - 16 each.
During the 1950's and 1960's, Norm Smith coached the Melbourne Football Club to 6 Premierships over 11 seasons, with 11 consecutive finals appearances! Those were the days when only 4 teams made the finals. None other has even approached that kind of record.
Essendon and Carlton with 16 premierships each.
East Fremantle with 29 premierships
Michael Tuck (Hawthorn) 7 premierships
As of May 2011, Essendon and Carlton share the honor of having won the most VFL/AFL Premierships with sixteen apiece.