Kinnear questioned calls for an independent regulator and transfer levy in his programme notes in the wake of the emergence of the report, which was led by former sports minister Tracey Crouch.
Ex Manchester United defender turned pundit Gary Neville hit out at the comments on social media while the Football Supporters' Association voiced their concerns, saying Kinnear had "undermined" the report.
Crouch described Kinnear's complaints at two of the 47 recommendations in particular as a "tad extreme" after he used a comparison to 'Maoism'.
The Leeds executive has now addressed the fallout from his words in his Brentford programme notes, stating he passionately believes in the English football pyramid but again questioned government involvement in the national game.
"My questioning of the Fan-Led Review of football Governance expectedly divided opinion, I understand the calls for independent regulation and wealth distribution, but proponents of the proposals should not have to rely on the cliched narrative of 'self-interested suit' versus 'true supporter' to undermine the validity of the counter-arguments," Kinnear wrote in this weekend's matchday programme.
"I write from the platform of being a football executive, but my beliefs on competition and governance come from being a lifelong supporter and the two roles are not mutually exclusive.
"I cherish the English football pyramid from its grassroots - where I have managed a club to mid-table mediocrity, after disgracing most pitches in the North Home Counties Sunday League for two decades as a player - to league football, where I have followed Luton Town across five divisions and watched them play at over 100 wonderful and eclectic grounds.
"I passionately believe this pyramid strengthens and grows through a spirit of unadulterated competition, which encourages and rewards responsible and skilled management both on and off the pitch.
"Prominent commentators claimed my opinion on wealth redistribution would not have been the same if Leeds United were still in the Championship, but they couldn't be more wrong.
"The proof of this is that when we were members of the EFL, we were not focusing on the hand-outs or redistribution but, among a small number of other clubs, were challenging what we believed to be a woefully undervalued EFL media deal.
"We worked actively on how it could be better packaged and marketed to deliver significantly greater and fairer value to all clubs.
"Simultaneously, we were tirelessly improving every element of the running of our club to compete more effectively in player recruitment, development, coaching and supporter engagement to give Leeds the competitive advantages that would ultimately get us promoted.
"I believe competition, unfettered by government control and undistorted by non-merit based hand-outs, is the heart of a flourishing professional pyramid that inspires and funds flourishing grassroots.
"The notion that it might not be such a good idea to partially hand over the keys of our national game to the same government that has just blown £37 billion on Track & Trace worth of consideration, not outrage."
Palace chairman Steve Parish and Aston Villa chief executive Christian Purslow have also recently criticised elements of the recommendations, which were summed up in 10 key points.