It's like they expect me to spread their open position with my friends/peers, and while it's good to know of open positions, it is not my duty to refer my friends to them, and it's kind of rude.
I do not interpret that particular behaviour as rude, and I'd like to provide two explanations:
1) They may be legally required to do so: In some places, trying to snatch employees away from their current position by directly addressing them with a better offer can be considered illegal, hence headhunters circumvent such restrictions by not asking whether you would like the job, but whether you happen to know someone who does. Reading between the lines, they of course want you to consider the position.
Now, in that case, it is not at all rude for them to ask you whether you know someone who might be interested. It is simply careful wording, and should not be misunderstood as a request or even a command to actually look for someone else.
What is rude here, if anything, is the fact that they are sending you unsolicited messages in the first place. Spam e-mail and cold calls are a severe nuisance, and in that respect, offering jobs is not any different from offering products of any kind. Given that you signed up with LinkedIn for the very purpose to be findable and contactable with respect to the job market, this is kind of a mixed bag, though.
2) While you may feel flattered by being addressed in the message, the person offering the job also has a need to find someone for the position. They are aware that whoever they write to might not at any given time be ready or willing to change their job, but chances are they are in contact with other people with a comparable skillset. Hence, kindly asking you to pass on the offer if you happen to know someone suitable totally makes sense from the recruiter's point of view in terms of increasing the success of their offer, and once again should not be mistaken for an order to actively search for someone.
Conversely, it may be the case that you do happen to have friends who are looking for a position. Asking you to pass on the offer just saves you the effort of finding out whether the recruiter in question would allow you to show the message to someone else. Seen like that, I would actually perceive such a request in a recruitment message as a positive sign, as it shows the company is not an uptight place that hammers down merciless confidentiality rules on every tiniest bit of communication. Likewise, it implies that at least they do not use shady practices such as making you one offer, while making someone else a substantially different offer (which, based on a thorough background check, is still good enough for them, but considerably worse than what you were offered) - the offer you received is the offer they want to make to their employees, it's not an offer that was tailored to convince you, and only you, of joining.