I believe Fiverr TOS doesn’t allow that to prevent people from communicating outside of Fiverr. Sharing a Facebook ID, LinkedIn profile increases possibilities of communication out of Fiverr. There are chances of some users abusing this and ending up with doing business outside of Fiverr (which lowers down Fiverr sales which obviously Fiverr wouldn’t want).
You can actually be your authentic self without the need to place your FB and LinkedIn profiles. I think the way one puts up his gig, his portfolio and his overall Fiverr profile will reflect on his level of professionalism and buyers more or less can see if one is being authentic enough.
Although some people may lie and be inauthentic in their skills, education and certificates earned and possibly get reported or suspended, that is their cross to bear.
You can share absolutely just that, it’s seen under Education and Certification. If one is lying about it, then that’s when it becomes not authentic. Just like in the link you shared, there may be a time Fiverr staff asks you a certificate or diploma and you can present them easily if one is authentic.
If you want to take your “authenticity” a level further, you can apply for Fiverr Pro. Fiverr staff will manually check the skills, education, work and etc the applying seller provides. Once accepted you are advertised as “Pro” and that’s as authentic as you can get here on the platform.