well one thing that helps monk is the option to swap out their set feats (pg 19 of OA) for things on table 6-1 (on page 79 of OA), though they must met the pre-requisite feats to do so. Other than that true a multi-classed fighter/monk will be able to get MA mastery easier, but the same is also true of fighters and feat chains.
Most character can barely finish certain feat chains and fighters can end up with 2 or maybe 3 feat chains (which may also include a MA Mastery as well, now there is a sick thought)
Also look at this way, most of the MA styles have skill requirements that a single classed fighter can not met until around 4th to 6th level.
Empty Hand style
Monk of min 6th level (1st Monks virtual unarmed strike, 1st power attack, human Sunder, 2nd level sub Ki shout for deflect arrows, 3rd level fists of Iron, 6th level: Eagle claw)
Fighter of min of 4th level for feats and skill requirement
Mighty Works
Monk of min 3 Level (1st level virtual unarmed strike, 1st level stunning attack, human: Improved Grapple, 1st level: Choke hold, 2nd level class: Deflect arrows, 3rd: Fists of Iron)
Fighter of min 8 Level (Because of stunning fist prerequisite of BAB +8)
Mighty Works 2
Monk of min 9th Level (Class 6th level: Improved Trip, 6th level: Iron will, 9th: Earth's Embrace, 9th: Ki Shout)
Fighter of min 9th level : (Due to the fact that Choke hold requires Stunning fist as a pre-req and the fighter would have picked up stunning fist at 8th level)
Foot and Fist
Monk of Min 3th level: (1st level virtual unarmed strike, 1st level: Power attack, Human: Round about kick, 1st Sub Stunning attack for Flying kick, 2nd Deflect Arrows, 3rd: Fists of Iron)
Fighter of min 7th Level: (Due to skill requirement)
Meditation of War
Monk of min 9th Level: (1st level virtual unarmed strike, 1st Stunning ability, Human: Anything, 1st: Anything, 3rd: Anything, 6th: Falling starstrike, 9th: Freezing the life blood)
Fighter of min 10th level: (this is due to the fact that both Falling starstrike and Freezing the lifeblood require stunning attack which has a pre-req of BAB +8 and thus you'd need your 9th level and fighter 10 feat to get them)
I think i've show monks can actually achive MOST of the style faster than a fighter due to the swapping the class feature allowed in OA