That makes no sense to me.
Even allowing that a thief could greatly benefit from an invisibility potion... Having the innate ability to create one seems kind of absurd to me.
I'm not against a mage/thief style character, but I will be if the thief gains ability in magic for increasing thief based skills.
These skill sets should be utterly separated. The guy that becomes a mage or alchemist is clearly well off enough to not need to work; while the guy that is out thieving all night doesn't have time enough to study the books and experiment. Anyone that actively does both should progress at half the rate of those that focus their 'all' in just one discipline. (less than that if you count sleep)
It's because Stealth is more than just a thief. Alchemy is a science, it is like chemistry for cavemen. There is nothing mystical about it, a poisonous mushroom is not 'enchanted' it is just venomous. A thief may use alchemy for invisibility, or nighteye, or chameleon, or speed, or acrobatics, or health, or magicka if it is a mage/thief hybrid. An assassin would use it for all of these and poisons like Paralysis, damage health, etc. A mage would almost never fight hand to hand so it would only need potions for restoring magicka and health.
When it boils down to it look at Oblivion. What character was most likely to make a bunch of potions? A mage, because it was a magic school. Would he use a fortify blade potion? No as he casts spells. Would he use a poison? No, he casts spells. Who uses most of the potions that can be made? A stealthy character.
The same thing happened in real life history. Those who were once hailed as witches with magical potions resurfaced as doctors with medicine. The world of Nirn merely evolved intellectually, and sees Alchemy as a science, not an art.