The invitation services are registered tour companies in the respective countries, so the invitations they issue are perfectly legitimate. Technically they're exploiting a loophole in the law, but many of these companies have close relationships with their local embassies so it's not like they're doing anything surreptitiously.

I've always used one of these companies (actually I've used several over the years), not just to issue the invitation but also to process my visa on my behalf. The £30 or so mark-up they charge on top of the Embassy visa fees is well worth it, considering I can do everything by post and I get my passport back even faster than if I'd submitted it myself.

Of course, if it wasn't so hard to get a visa for independent travel (without prior hotel bookings) in these countries, or private visas for visiting friends and relatives*, there would be no need for anyone to exploit these loopholes.

*though, to be fair, the Russian government has recently changed the private visa rules so that Russian nationals can issue invitations for their own family members at foreign consulates, which means I'll no longer have to use sneaky tourist visas when travelling with my better half.