If you haven't done so already, sit down and explain your game to the player and how stat generation and such goes in your games.
She has a valid point, and one that doesn't signify immaturity at all. If she's played in the type of games where everyone has high average stats, that could explain where she is coming from. Same if generation is like 5d6 or 6d6 per stat, reroll 1s, keep the 3 best. I''ve also played in games where DMs give you 80pt buy and you build your stats up from 1--which is close to all 15s at a 1:1 cost.
Explain to her that PCs aren't superheroes in your games, that 18s are truly exceptional and rare and aren't as simple as just a 16 and two +1 bonuses at 4th and 8th to achieve. And, maybe she's been playing in games where stats are on kind of an epic scale.
To answer the topic question, I'd say anything under an 8 is too low. Its interesting to play characters with flaws, but below an 8, a character is either a cripple or a retard and has no business out adventuring because they're in for a short career destined to end at a discharged trap/spell, hacked to pieces, or in some monster's stomach. Below average stats aren't 'interesting', they are liabilities and weaknesses that sooner or later will be fatally exploited.
Of course, it also depends on the style of play you do as well. If you're playing a game with little investment of their characters from the players, stat generation shouldn't matter much. But if you're dealing with players that get emotionally invested in their characters and they're expecting to play them for a considerable amount of time, then sit down and discuss with them what kind of character they want to play.
If everyone has at least average scores, then you could come up with a method to reflect that as well. Maybe something like this:
You could pair up stats (Str/Con), (Dex/Int), (Wis/Cha). Have 3 categories; focused stats that the character trained in extensively, practiced stats that the character developed somewhat, and average stats. Allow them to assign a total +5 modifier to two focused stats (+3/+2 or +4/+1), a total +3 modifier (+2/+1 or +3/+0) to practiced stats, and a total +1 modifier (+1/+0) to two average stats, with the actual scores being the even number values for the chosen modifiers, so no stat is less than 10, and none higher than 18. How to handle racial adjustments though? If a stat has a racial bonus it can be any stat (focused, practiced, or average). If a stat has a racial penalty, the penalized stat must be in the focused or practiced category, otherwise an average stat penalized results in a character that is just too weak, slow, puny, stupid, ignorant or disliked to be an adventurer.
Of course, this just leaves you basically with four arrays to choose from:
18, 16, 12, 12, 10, 10
18, 14, 12, 12, 12, 10
16, 16, 14, 12, 10, 10
16, 14, 14, 12, 12, 10
But its all in the presentation. Arrays aren't appealing because the values are fixed in front of your eyes for all of the stats. You get to assign them as you want, but you have no influence over what numbers you have to choose from. But if you offer to let them choose as I suggest above, the results are the same as the array, but the player gets the illusion of being able to choose their individual scores--and without being 'penalized' as with the point buy method where you have no choice in getting below average or nearly all average stats for 1 high score and maybe 1 more above average. Plus they don't get to whine/gripe/bitch about bad rolls either.
