In Oblivion, when you create a custom class, you need to choose a specialization from Combat/Magic/Stealth. I saw a website recommend Magic for a stealth assassin. How does that give a stealth player a better advantage than a Stealth specialization does?
Spells that I'd find particularly useful in Assassin characters are the Chameleon and Invisibility in the School of Illusion, and the Open Lock & Buoyancy skills in the School of Alteration.
The Illusion skills allow you to escape after taking down your mark. The Alteration skills allow you to get to your mark in ways you may have previously been denied.
The recommendation for Destruction skills I assume is to just allow some damage dealing without having to rely on heavy weapons, that may weigh your character down.
Since that website doesn't really give any details, we can only guess as to it's authors intent.
When you're occupied assassinating you might lose sight of your levelling. Deliberately not using stealth as your specialization will let you hone your skills more slowly so you don't accidentally "waste" too many skill increases.
Oblivion's levelling system is a bit weird. Because the skills in your specialization (and more specifically your class skills) are what make you level, everyday adventuring can make you level faster than you actually want to – because the world levels up with you. This can result in having a character that is good at a few core things, but because their other, non-core skills are low, they are unable to win against "equal" level opponents. As a result, it is common advice among serious players to put your specialization and (class-skill choices) in skills that you won't use very much for your character type, so that you can increase your real core skills without causing level-ups and causing the opponents to increase in difficulty. Then, when you want to level up, you grind your useless "core" skills to trigger level-ups. Magic is a particularly easy category of skills to grind, since many spells don't need a target to trigger skill increases.
There are many ways that magic can help a stealthy assassin, but specializing in it and just playing normally will only cripple your character. Thus, it's far more likely that this advice you read is part of the sort of controlled levelling scheme that hardcore Oblivion players use to carefully manage character growth and world difficulty. The quote:
...is a large clue, along with their skill-gaining advice, that this sort of controlled levelling is what they're talking about.