Partly true, but mostly total bollox. It would still be a very good idea to have your own website.
Reasons:
You are in complete control of the content and can put anything you like there without falling foul of somebody else's rules or latest agenda.
On social media they control all. You control nothing. With your own website, only you are in control.
The social media websites can go down and may even disappear one day for a number of reasons.
Not all social media shows up in Google or other internet searches. Your website if managed correctly will come up in the searches on the internet you want it to.
You can advertise a particular part of your website on the internet or elsewhere setting your own rules around this.
Only you can lock yourself and restrict your own access to your own content with your own website.
If you lose your website log-in details you can obtain them again in seconds from your hosting provider.
And so on..............................................