Your sources do not support your argument.
The initial source is in regards to whether stats increased by stat items count towards prerequisites. The fact that it works is simply because of the rules posted later in that same thread, not because items on their own count towards prerequisites .
This thread is not even about pathfinder but 3.5 (or an earlier edition). Despite pathfinder being based on 3.5, they do not work the same.
These comments touch on why scrolls and wands are not valid, in that wands use the spell trigger activation method, instead of the character casting the spells. If we go the the rules for the spell trigger activation method, we see that it falls under "Using Items", which is not "casting spells".
Here is an FAQ that shows even more that casting spells from a wand, does not count as your character casting spells:
Items as Spells: Does using a potion, scroll, staff, or wand count as "casting a spell" for purposes of feats and special abilities like Augment Summoning, Spell Focus, an evoker's ability to do extra damage with evocation spells, bloodline abilities, and so on?
No. Unless they specifically state otherwise, feats and abilities that modify spells you cast only affect actual spellcasting, not using magic items that emulate spellcasting or work like spellcasting.
As for racial spell-like abilities qualifying you for the class, there's an FAQ for that:
Spell-Like Abilities, Casting, and Prerequisites: Does a creature with a spell-like ability count as being able to cast that spell for the purpose of prerequisites or requirements?
Only if the pre-requisite calls out the name of a spell explicitly. For instance, the Dimensional Agility feat (Ultimate Combat) has "ability to use the abundant step class feature or cast dimension door" as a prerequisite; a barghest has dimension door as a spell-like ability, so the barghest meets the "able to cast dimension door prerequisite for that feat. However, the barghest's dimension door would not meet requirements such as "Ability to cast 4th level spells" or "Ability to cast arcane spells".
As such racial SLAs do not qualify you for being "able to cast 2nd level arcane spells". I'm fairly certain you understand this (given the link text), however, I am clarifying this just in case.
There are only three methods that help both arcane and divine casters with entering Mystic Theurge at level 4 that I know of, and two are mentioned in the question you linked:
The first way is with the equipment trick (Sunrod) feat:
Like the Sun: You can use a sunrod as an additional material component for any spell that bears the light descriptor. The spell is treated as one spell level higher (to a maximum of 9th level) for all purposes, including the calculation of saving throw DCs and its ability to overcome sources of magical darkness.
This allows you to be treated as if you can cast spells of 1 spell level higher, letting you be treated as if you can cast 2nd level spells in both of your classes. In fact you'd be able to qualify for Mystic Theurge at level 3 if not for the fact that you need 3 ranks in Knowledge (Arcana) and Knowledge (Religion) prior to taking it.
The second way is Eclectic and Esoteric Training from Inner Sea Magic:
Eclectic Training (5 Fame): Guilds often require members to master and train in different subjects. When your Fame score in a guild reaches 5, choose one spellcasting class you have at least 1 level in—you increase your effective caster level in that class (including the number of spells you know and can cast per day) by +1, to a maximum caster level equal to your total Hit Dice. Single-classed spellcasters should still pick a class to which this bonus applies, since this bonus is retroactive.
Esoteric Training (35 Fame): The bonus to caster level you gain from Eclectic Training increases to +3 (but is still limited by your total Hit Dice). You may select a second spellcasting class to gain a +1 bonus to effective caster level.
This allows you to scale up your ability to cast spells, if you can gain the necessary fame and benefits to use it prior to level 4, thus allowing to enter Mystic Theurge at level 4.
Or the Shield of the Sun:
This +5 Large shield, emblazoned with the symbol of the sun, allows the wielder to cast spells as if she were a 20th-level paladin with a Charisma of 20.
If you have this shield when you hit level 4, you can take Mystic Theurge assuming you're a prepared arcane caster, and able to cast 2nd level arcane spells.
Additionally, there is at least one item that can help you enter earlier than the normal 7 (though not at 4), such as the Candle of Invocation:
A cleric whose alignment matches the candle’s operates as if two levels higher for purposes of determining spells per day if he burns the candle during or just prior to his spell preparation time. He can even cast spells normally unavailable to him, as if he were of that higher level, but only so long as the candle continues to burn.
This allows you to be "able to cast divine spells of the 2nd-level" and help you enter the class faster. Despite this, as it only affect one side of casting, you're still unable to enter the class at level 4.