I believe the Finch Primer to be, charitably, a reactionary overcorrection towards corporate D&D.
The following four points are intended to replace those made by the Primer.
The Primer mistakenly attempts to claim that rulings are preferable to rules, which is not true. Any worthwhile ruling becomes a game rule. What corporate D&D has done is attempt to present a holistic system that must not be deviated from, and whose rules must be adhered to even if they do not make sense or where game situations would clearly take precedence. The game rules are treated as giving rise to the physics of the game world. Instead, in old school play the game world exists first and the rules act as an overlay.
The Primer further implies that all game problems are solved diegetically in old school play, which is absolutely false. Rules provide a common ground for players to understand complex situations such as combat, and allow common game situations such as lockpicking to be resolved consistently. Diegetic solutions are possible, and often desirable, but these are special precisely because they are exceptional.
2. Player Skill > Character Sheet
The Primer mistakenly suggests that player skill does not include effective use of character abilities. This is simply false. However, it is true that corporate D&D is badly designed, insofar as it includes abilities on the character sheet which inform players what they should think and how they should act, favoring a style of roleplaying that is in direct contradiction to successful play.
Moreover, modern systems often include a huge array of character building options which are poorly balanced, and in fact impossible to balance. The result is a dysfunctional game that cannot be played as a game, leaving players with little recourse except to engage in play-acting rather than earnest gaming. Because this is not the case in old school play, the point the Primer makes is irrelevant and incoherent.
3. Superheroic Play
In old school play, character progress to superheroic stature by gaining levels and acquiring magical treasures. In modern corporate D&D, in order to guarantee a certain consistency of play, the powers previously afforded by magic items have been baked into character levels.
The Primer mistakenly reacts to this guaranteed suite of powers by insisting the characters never obtain such abilities. This is incorrect. Characters should reach higher levels and should obtain fantastic magic items. So-called "Mudcore" permanent level 1 play is unenjoyable and to be shunned.
4. Fair Play
The Primer falsely claims that game balance does not matter. This is only true insofar as game situations might be entirely impossible to overcome via combat, and retreating in the face of excess danger is expected. This often called "Combat-as-War" in old school play, as opposed to "Combat-as-Sport" in new school play.
Nonetheless a certain fairness is expected. The game is still a game, with players facing challenges that they might reasonably find a way to overcome or move past. The game is exactly in the form of a tournament in which the players face off against the content which the referee has prepared. Misapplication of game rules may in fact break the game, and in such cases adjustments can be made to correct the course of play in the interests of fairness.