It means that the Hollis authorised dealer will do the service, charge you for that service and if they fit parts they are free. If you miss a service in one year you lose the warranty totally. Dishonest LDS techs will do a "test" (does it breath ok) and call it a service (seen it done and I was shocked that the charge was $135 for that). Honest ones will do a proper yearly service and provide parts. The idea behind this offer (I believe), is to ensure the LDS gets more than to sell you a reg, but to continue to sell you servicing, thus ensuring the LDS will stock their regs over other brands, The actual true cost of parts is miniscule compared to what they are charged out at. With one of my Oceonic regs, I think the AUD cost for kit is about $35, and it has a plastic seat, a couple of O rings, 1 zip clip and a SS nut, worth perhaps $1 in practical terms. The free parts is a bait to set the hook of paying yearly servicing costs. As you are not an "Authorised dealer" you cannot service your own regs and still keep the warranty.
Understand what you are generally getting for your money, a service with free parts, does not always equate to a full pull down, clean and rebuild with new parts.
For me, (although I do my own servicing), I work on the theory that any quality reg (from new) will run for around 5 years (at least) without servicing (if treated with care and washed), and usually shows signs of free flowing secondary or intermediate pressure creep on the primary as the first issue. Thus you save 5 years of service costs amounting to some $135/year (in OZ), thus after 5 years you could junk many reg sets and buy new ones from the savings, or simply get a full service and pay the full cost of labour and parts.
My thoughts as to the scare mongering of if you dont get them serviced yearly or you will die, is that if a reg set for average use with care taken, if its so unreliable that it will fail after 1 year of service, I would not buy them. I have some 10 reg sets and non get yearly service, and only on a couple of odd times have I had free flows that require a service. I have however had a number of regs fail spectacularly after a service by LDS (hence why I did a Dive tech course and now service my own).
If you want peace of mind however, I recommend servicing yearly (from a competent LDS or authorised dealer) as you are then paying for risk reduction. When I was paying for servicing, I did find a big difference in quotes on servicing, the trick however is guaranteeing quality work.
If you are like me, and prepared to take a small risk, and know your gear sufficiently to be in tune with how it operates and have the feel for service periods, then you could service 5 yearly or as required earlier. If your regs get flooded or show signs of operating different, then get them serviced.
I had a Diverite Oxygen reg used maybe 6-8 times show pressure creep in the first stage, serviced it (costing about $20 AUD for the kit) and its now fine. Had I got it serviced at a reliable LDS, the probable cost is in the order of $35+$35+$20 which is getting close to the price of a new primary reg, given the whole setup was about $300 new. So something else to consider.
The above is my thoughts, and I am sure others have differing opinions, but keep in mind, you are responsible for your diving safety, so you need to be comfortable with your gear. I am happy with how mine performs and I service 5 yearly or when a problem arises. If you treat your gear like crap, or are at all nervous about it, then get it serviced as per the manufacturers suggestions.
In the end the choice is yours, and you are the one who has to be happy with the result.