All manufacturers specify similar. I think it's BS. Cars don't go off. I only service by mileage.
Lucky I do not eat cornflakes while reading geekzone or I'd be coughing them all over my desk.
Folks have already mentioned oil and brake fluid but there are loads of things that most certainly do go off.
The worst offender is the cam belt. The are generally specced to something like 100,000 kms or 5 years. If you do 10,000 kms per year then I would expect your belt to fail well before the 100,000 mark. The same is true for other drive belts such as those for the water pump, power steering pump, air con etc. The culprit is the slow oxidation of the organic compounds - synthetic or natural rubber. This leads to cracking, hardening and embrittlement.
Tyres are also affected by that process and also UV exposure. It's not a big deal on rwd cars as the tyres will never last long enough unless the vehicle is a real garage queen. It can be a problem for fwd cars if the rear tyres are left in place forever as they will wear so slowly that they will start to crack and harden while still having loads of tread. Also, beware of the famous 'spare unused' because it is quite likely also unusable.