Heck, I get these calls regularly myself. I enjoy challenging the people on the other end of the line, and very quickly one thing becomes clear.
They’ve no idea what they’re talking about.
SEO, sadly, isn’t a regulated industry, and because of the level of investment people put into their online presences it’s very easy to frighten them with bogus information.
The people emailing and calling are sales people; often for firms that with a bit of digging, you can find myriad horror stories about online.
My favourite examples of their spiel include, “Your site doesn’t have keyword tags” (search engines don’t actually use them) and “Your site isn’t W3 compliant” (Google has made it clear this has no effect on a site’s ranking).
The latter is particularly nefarious, because although a W3 compliant site is certainly best practice–very few sites do tick all the boxes.
It’s scaremongering at its worst.
Remember, when you get a call out of the blue, or emails that by rights should go straight to your spam folder, always check with a known professional, someone you trust. And if you are considering working with a new company, ask how many sales people they have compared to actual SEO experts on staff.
Do some checking, to make sure what they’re telling you is true.