They're not saying that they're the registrar. They're just saying that they'll register the domain on your behalf. Lots of hosting companies do this.
If another company registers the domain for you, the domain may not be in your name (you should at least be listed as the registrant, and possibly also the administrative contact.) If the domain is not in your name, then you won't truly "own" the domain and you won't be able to take it with you when/if you change hosts.
This particular host may, in fact, put the domain in your name. This would mean that if a dispute ever arose - they tried to keep the domain from pointing to your new hosting account if you switched hosts, for instance - you would be able to contact ICANN and argue that the domain is in fact yours - it was registered and administered in your name, there's your name in the registrant information to prove it. I have never gone through this process before, so I can't give you the particulars of how this would work - but that's the theory, anyway.
It's possible that this host would put the domain in your name, and would in fact allow you to transfer the domain away from them if/when you change web hosts. That's how I operate - the client requesting the domain is the registrant, TLM Network is the technical/billing/admin contact, and if/when they want to transfer away I will give them whatever assistance they need to get it transferred. (I won't keep administering the domain after they've left - but I'll gladly help them transfer it to the registrar of their choice.)
If you want to take advantage of their domain registration service but want a little bit more assurance, you could always ask them to create a brief contract stating that they're registering domainx.com (or whatever) in your name, such service to begin on this date and end in that date unless you specifically request renewal, et cetera, et cetera. Just tell them that you're a little bit nervous with all the other horror stories you've read about companies holding domains hostage, that you really don't understand how the proxy-registration system works and what your rights/obligations are, and would like to have something that spells this out for both parties. This should work well - you're not saying "I think you might be a crook", you're saying "There's a lot about this system that I don't understand - can I have a brief contract that tells me my options and obligations in this particular transaction?" This will give you piece of mind, may give them something else they can use with their other domain registration clients, and gives you something tangible and concrete in case some dispute should develop later on
