Before April 17, 2022, the answer is no, that is not true.
After April 17, 2022 and until now, the answer, unfortunately, is yes, that is true.
The reason given — most people weren’t using the level 1 charger — may be valid (there is some data that suggests otherwise, but it’s not complete), and you can always buy it separately from the Tesla Store assuming they get back in stock if you need it. Or, if possible, you can get a level 2 charger installed at home (reference this and this, among other FAQ entries) before you get your car.
For those rare times when you might need it, or when it’s certainly more convenient to have it, while traveling, the answer of trying to buy it from the store when it’s back in stock still holds, but also refer to this FAQ on how to find where chargers are. There are many out there and more coming every month, this mostly becomes one of convenience. It’s quite true that having to go somewhere to wait several hours for a level 2 charger is not convenient if you’re on vacation somewhere.