"John Doe" above is not a public figure - your parent's point is that social media enjoys all the advantages and power of newspapers without bearing any of the responsibility to strive for truthfulness.
In fact IMO it's even worse - unlike newspapers which would at least be embarrassed by blatant mis-reporting, sensationalist and fantastical stories are a major source of profits for social media, and they've got incentives to encourage and promote them.
Yes, most mainstream publications do strive for truthfulness (fortunately) but it's not really a requirement for 1st amendment protection and I'm sure we can think of fairly mainstream news outlets that don't let the truthfulness responsibility cramp their style too much.
In fact IMO it's even worse - unlike newspapers which would at least be embarrassed by blatant mis-reporting, sensationalist and fantastical stories are a major source of profits for social media, and they've got incentives to encourage and promote them.