I'm 'wholly' Russian and I've never considered what you state above as specific to - or even particularly prominent in - Russian culture. In almost any society, if you were to refuse a personal gift, it would be considered rude and insulting. So, firstly, I'm confused as to why you single out those particular cultures. Secondly, it's a spurious comparison because this is a company trying to make amends for inconveniencing its customers and providing them with a faulty product - there's nothing personal about it (despite what Jobs might say about taking things 'personally'), and clearly no one is going to be offended if the offer of the free case isn't taken up (in fact its not even something you have to 'opt out' from, but rather you have to 'opt in' to take advantage of....I have no idea why I'm taking apart your flippant logic). As you yourself said, somewhat contradictorily given the point that followed, 'Apple doesn't have any feelings, it's a company'.
The way you express yourself is ridiculous, but your essential point is still sound. Apple is an enormous company with a very sizeable profit margin on its products (a bigger one than most I'd suggest - they take advantage of the fact that we're willing to pay those premiums, as is there right). It can easily afford to hand out 1 free case to every iPhone 4 user (otherwise it wouldn't have made the offer).
There is nothing morally wrong about choosing to take advantage of this offer even if you don't have an obvious antenna issue. The free cases aren't primarily about fixing a design fault. Obviously I don't know what Jobs thinks (and knows) about this issue privately, but publicly he's stated that the signal 'attenuation' isn't a big deal, even with 'naked' phones, and is only a problem for a minority of users, in a minority of situations. Yet he's still offered every user a case, and without having to provide proof of any problems. Jobs said: 'If you want a case, we'll give you a case'. This is about Apple placating angry customers and saving as much face as possible - so they lose as little money as possible. Its intentions have nothing to do with generosity or 'doing the right thing'. They figured they would lose less money making this gesture than not making it.
BoxerGT2.5, if you don't want to take up the offer, then don't, but don't judge those who do simply because they can. Being truly immoral about this would be to somehow circumvent their system and get a case for free (to sell on ebay) without also having purchased an iPhone, or somehow deceiving their online form to get several free cases. Furthermore, if you're concerned about slipping moral standards amongst the 'youth of today', there are far, far more important issues to worry about than people signing up for a free $30 case they are legally entitled to, even if they don't strictly need it.