To answer the question if the domains are owned by a rock solid company: yes, they do.
The subdomain services are provided by CentralNIC who have been in the business for 10 years or even longer. They never had any issues with expiring domains, hijacked domains, crashed servers etc. So the subdomain owners never experienced any more threats than with any "real" domains. Personally, I'd consider CentralNIC as solid as the average "real" domain registrar, and I would trust it more to register a CentralNIC domain than to invest in some obscure ccTLD where policies of foreign registrations may change very soon.
However, the price is a turn off and stops me from buying domains at CentralNIC, even though I do believe extentions like .uk.com and .eu.com have potential. But to ask more money for a subdomain than for a real .com or .co.uk i a few bridges too far for me. The day CentralNIC drop their prices I will probably buy a few subdomains, however I am not willing to pay more than a few euros.