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Water Bob
Page 11 of the AD&D DMG says this:
As AD&D is an ongoing game of fantasy adventuring, it is important to allow participants to generate a viable character of the race and profession which he or she desires. While it is possible to generate some fairly playable characters by rolling 3d6, there is often an extended period of attempts at finding a suitable one due to quirks of the dice. Furthermore, these rather marginal characters tend to have short life expectancy - which tends to discourage new players, as does having to make do with some character of a race and/or class which he or she really can't or won't identify with. Character generation, then, is a serious matter, and it is recommended that the following systems be used.
The book then goes on to list four possible systems: 4d6, drop lowest, six times, arrange as desired; 3d6, twelve times, keep six best, arrange as desired; roll ability scores in order, but 3d6 six times for each one, keeping the highest roll for each score; roll ability scores in order, using 3d6, twelve times and keep the preferred set.
There is no discussion of re-rolling if there are not at least two 15s. The comment in the PHB (p 9) that "it is usually essential to the character's survival to be exceptional (with a rating of 15 or above) in no fewer than two ability characteristics" is followed immediately by this:
Each ability score is determined by random number generation. The referee has several methods of how this random number generation should be accomplished suggested to him or her in the DUNGEON MASTERS GUIDE. The Dungeon Master will inform you as to which method you may use to determine your character's abilities.
Given that none of those methods, as presented in the DMG, allows for rerolls if there are not at least two 15s, I would be inclined to take the remark in the PHB as a descriptive/predictive rather than normative one.
Another relevant consideration in generating ability scores in AD&D is that an ability score of less than 6 confines the character to a particular class (STR - magic-user; INT - fighter; WIS - thief; DEX - cleric; CON - illusionist; CHA - assassin). This means it is possible to generate ability scores that preclude taking up any class, either because there are two scores below 6, or because there is a single score below 6 but the character doesn't otherwise qualify for the class in question (eg a character who has only a 5 in STR and only 8 in INT does not qualify to be a magic-user, but may not be of any other class). In such circumstances is a player expected to re-roll? Or raise a score to the minimum that will allow taking on a character class? The rules don't help answer these questions.