I mean, maybe they're going for the social dissaproval angle - you can stop people from hoarding masks by making it socially bad to wear a mask, but that seems misguided if true.
If there were an infinite supply of masks the advice would be entirely different.
So, some protection is better than no protection. Consequently, It's difficult for me to understand why discouraging people from using face masks is a good idea.
Use it properly and keep social distancing, while regularly cleaning your hands.
If you're sick but don't know it, your coughing/breathing is spreading the virus.
So everyone wearing a mask prevents the infected, including those that don't know that they're infected, from spreading the disease.
And for those who are not sick, it may offer small protections.
Tiny downside for a large upside.
"If you are healthy, you only need to wear a mask if you are taking care of a person with suspected 2019-nCoV infection."
https://www.who.int/emergencies/diseases/novel-coronavirus-2...
"If you are not sick, do not buy a face mask. If you have one already and you are well, it is not recommended that you use it."
https://arstechnica.com/science/2020/03/dont-panic-the-compr...
Is this in your opinion "false information"?