What? In the 1e UA, where drow were introduced as a PC race, the maximum level male drow could reach as a magic-user was 12 (or higher, with an Int of 19 or greater). That's a higher maximum level than any of the other elven subraces. (Female drow sucked as magic-users, but were better fighters or clerics).
If I might nitpick, the text of
Unearthed Arcana stated (p. 8):
Important: The level limits given and implied in the sub-tables may be exceeded by 2 in all cases where (a) the character is single-classed and (b) the class in question could be a multi-classed choice for that character. Examples: A hill dwarf fighter/cleric with 18 strength can advance only to the 8th level as a fighter, while a hill dwarf with the same strength who was a fighter only could advance as high as 10th level. A hill dwarf cleric/fighter with 14 strength can attain 6th level as a fighter; if the character were single-classed as a fighter, he or she could advance to the 8th level in that class. A half-elf cleric/ranger with 18/90 strength, 18 intelligence, 18 wisdom, and 18 constitution can attain 9th level in the ranger class, but a half-elf ranger with the same ability scores can rise as high as 11th level in the class. A dwarven assassin is restricted to the level limits shown on the table, since it is not possible for a dwarf to be both an assassin and a multi-classed character.
Now, that could get your dark elf character to 14th level as a magic-user if they had an 18th Intelligence, but that still brought up the problem of increasing that ability score in order to reach higher levels.
That particular chestnut was much harder to crack...mostly because it was unclear just how strict the racial ability score maximums were. They obviously applied to modifiers applied at character generation (including for NPCs,
according to the PHB errata, since NPC stat modifiers were sometimes different from PCs; notice how NPC elves received a +1 Intelligence, +1 Dexterity, instead of the -1 Constitution, +1 Dexterity that PC elves got; DMG p. 237), and they also applied to aging modifiers, as was explicitly stated on page 13 of the DMG.
Beyond those, though, there wasn't a clear indicator of whether or not those limits applied to other things that raised your stats, of which there were
many. While we're all familiar with the note about how
wish and
alter reality spells only raise a score by 1/10 value if the ability score in question is 16 or higher (DMG p. 11), but there are also various options such as a
tome of clear thought (DMG p. 155),
gem of insight (UA p. 100),
egg of reason (UA p. 100), a scarlet and blue
ioun stone (DMG p. 147), magical pools (DMG p. 172), and similar options.
And, of course,
Gary himself had ability score increases be "generally gained by adventure in which deities give such a boost to a single stat as a reward for outstanding performance, an artifact is gaines, [sic] or a wish used."
Presuming your DM didn't have the racial maximums be utterly impermeable limits, it wasn't unthinkable that a (male) dark elf (single-classed) magic-user could get his Intelligence up to 22, which would enable him to reach 20th level!
(Of course, it might just be like you said, and the note about them being "strong magic-users" is relative to other demihumans in general and/or elves in particular.)