You guessed it. Sun scalled is common with any young plants that are not exposed gradually to strong sunlight. All my seed pots get a week or more in my greenhouse to 'harden' them. off. Tomato leaves espcially are very soft and tender, and lack that familar odor. Once outside a week or so, the leaves will darken and become more like the firmess of outdoor foliage on most plants. My basil is small too, and some is only about 10 inches tall, but is under plant lights now. Soon it gets moved into the greenhouse where they get more sunlight, but because I can paint on a whitewash on the greenhouse glass roof, it will reduce the strong rays of the sun. Just give them sume shade during the hottest sun (overhead-noon) for a few hours per day. The leaves will not come back, but new leaves will take their place fairly fast.

When we talk about things like 'basil prefers full sun blah blah' we are talking about MATURE plants. As with human babies, plant babies need extra care and protection. All babies are tender and fragile and need to be toughened up as they grow. They need to be gradually exposed to the conditions they'll eventually learn to love. In horticulture-speak it's called 'hardening off'.

Provide adequate shade for your babies in the hottest part of the day, but let them be exposed for longer and longer periods to the full sun. A large potted plant which can be moved around is one way of doing it.

Is it possible that they were over-fertilized? I've put tiny (2 inch tall) basil plants out into the full sun in Georgia and they've done well. The other thing to consider is drainage. Mine thrive because what their roots reach down into where I am is almost all sand. The other possibility is that you may have a variegated basil, which won't be all green. If basil doesn't like the clay where you are, I've also had extremely good results growing it in pots. Good luck, and keep us posted on how you're doing.