I had read about the plan but never actually read the president's statement.

This was more than just a contingency though. There were a number of things that could have gone wrong. They thought the surface of the Moon was solid, but there were fears the lunar module might sink into the surface dust which might throw off the balance. They had landed other probes on the Moon so they had some idea, but the Lunar Module was heavier and if there were a soft spot, the lunar module might be out of position to re-launch. Same thing if the lunar module landed on a rock or hillside that could cause it to tip over.

The moon lander rocket could not use liquid propellant which needed a spark to launch off the Moon. Of course there is no air on the Moon, so creating a spark could not be done. So they used a solid propellant (chemical reaction) for the lander's rocket. The fuel used was so corrosive that it destroyed an engine on one firing so every ascent rocket in the Apollo program used an engine that had never been tested. I saw an interview where one NASA official was pretty nervous about whether the ascent rocket would work properly.

Then there is the garden variety malfunction (Apollo 13 was a good example), a lot could have gone wrong.

Eisenhower had a press release in case the D-Day landings failed as well.