I think everyone would agree with that statement as written. It's the economics that come into play. At 5 years, I wouldn't need much convincing to shelve a $300 helmet, but I'd need an iron clad argument to do the same with a $1000 Arai if all it needed was a new liner.
The style of helmet also plays a factor in absolute safety/protection and is a large factor (and it is not the only factor of course). As a common example for discussion, modular helmets are popular these days and they offer a lot of great features but try and find one that is Snell certified (few and far between, if any these days)??? There is a reason, they do not provide the same required level of face and chin protection as a full face (and roughly 1/3 of head injuries are face/chin) in their testing with the chin bar down--even worse chin bar up obviously (lots of data on all this BTW, it is science based not opinion)--even vs older Snell standards. They are a compromise vs full face all else being equal, absolute safety vs features and comfort--a personal decision. Of course open face and buckets are even worse in this context, no helmet worse yet.
Where am I going with this... In the end many of us (maybe most) are making a compromised decision based on economics, comfort, fashion, features, peer pressure, etc. Applying risk management (well or poorly) even if they may or may not know what risk management is, people still do it. Same with riding in jeans vs leathers, etc. The "safety first, must be new, must be latest tech, latest materials, $200 helmet for a $200 head, etc. etc." crowd that always comes out in these threads all sounds great but really should only be said by the ATGATT crowd that only use the latest Snell full face helmets while track riding solo on their speed limited Vespa, otherwise it is glass houses... Even then it does not provide any definitive answer on helmet age, sorry about that but for personal context...
I am a full face guy today but would be open to a modular in the future for my next helmet when mine is done. I also ride in jeans but also leathers but not ATGATT. But I also understand my properly fitting, more than 5 year old, Snell, un-crashed, not abused, not dropped, no damage, well taken care of, properly stored, properly cleaned, full face will offer at least equal protection than buying a spanking new modular helmet (based on science and testing) and still way better than the lesser options--open face....but maybe not as good as a new topnotch full face. At some point, condition, fit, etc. will push me to the next one, as did my other retired helmets did, whatever that is. No one should be riding in a poorly fitted or damaged helmet, goes without saying, or does it? But in summary new may be better same to same unless new is less than equal... is a modular dangerous, no, is it as good as a full face, also no.
We all have a risk inclusive hobby and we all have decisions on many fronts to make.