No. First, % chance to learn isn't "DM fiat."
I didn't say it was. Which spells the wizard gets are DM fiat though.
Second, when you gain a level, you gain a spell. (DMG 39) So, for example, the fabled attainment of 5th level means that, of course, the character will choose to acquire fireball ... and then throw out the character sheet when they fail.
Not sure which DMG you're looking at. The original blue header version has Item Saving Throws and Attack Forms on p39. And the spiffy updated one has Alignment on p39.
I kid.
But seriously, I have no idea what you are talking about. Yes, acquiring a vast number of spells could be a "game within a game" but what are you are describing is certainly not the RAW ... and definitely not the rule as most tables played them (which were fast and loose).
PS- TSR era had plentiful magic items, including scrolls. Which meant that there was always a surplus of spells to learn to from, not to mention spell books. For further references, see also TSR-era modules.
It's RAW according to my DMG.
“Once a character has begun adventuring, he won't be able to have additional spell books instantly appear each time he goes up in level. Instead, the player character must find some way to get additional higher level spells. As with initial spells, there are several ways this can be done. Any or all of these can be used in your campaign.” (DMG,p41/p61).
It then goes on to list several options. One option, if the DM picks it, is letting the player pick one spell when they level up or for the DM to randomly pick. It specifically says the character must roll to learn the spell if they pick it. So the DM picks which option to go with...so DM fiat. If the DM says you don't gains spells unless you find them in game...that's DM fiat. Then whatever spells they let you find is also DM fiat. What spells of that subgroup you get to
keep is up to a random roll.
There's even a section specifically about it.
"DM Control of Spell Acquisition: However characters acquire new spells, always remember that you are in charge. You have complete control over what spells the player characters get.
If a player character has a spell you don’t like or one that severely disrupts or unbalances your game, it is not the player’s fault. Who gave the character the spell? Who allowed it in the game? Controlling spell acquisition is an important responsibility. Consider your choices carefully." (DMG,p41/p61).
Bottom line, the DM chooses how the wizard gains spells and the DM chooses what spells the wizard finds in game. That's RAW.