It did not. The OLPC project wanted this feature, but it proved impractical to implement.

And what was the excuse for not including a solar panel on the back of the display to let the computer recharge in the sun?

The OLPC was a small device -- the usable space on the back was roughly 5" x 8". Even nowadays, this would be a very small solar panel; with early-2000s technology, it'd be completely useless. The project experimented with larger external solar panels costing $50 or more (roughly the same cost as the entire laptop!) and found that they were minimally effective for charging: https://wiki.laptop.org/go/XO_Solar

Because when the screen is visible to a user, the back of the screen is pointing at the ground, not the sun.

Here's a video of an external panel running the laptop: https://youtu.be/ITHNbOrPQyM

The idea is, when unused, the laptop could be left in the sun, where the back of the screen could trickle charge it without any user intervention.

Ideal? no. Better than having no power or using a crank? yes.