Why PR should work independent of Marketing?

PR Is more towards building +ve perception of a brand, where as marketing is considered to be bragging about your brand.
Its in Human Nature that if an individual see's a brand or anything related to it on any third party channel or by any report issued by third party it tends to believe it more compared to a company stating its USPs on its website.
Coming back to your question, PR enhances and presents your brand in a way that it appeals to masses and builds credibility .

I don't think that PR and marketing are different.
On the very contrary, PR and other marketing activities are closely related, and should work hand-in-hand.
PR is one of the branches of marketing – or one of marketing's "arms", as I like to call it.
PR should make use of the media, and people (the new media), to communicate your marketing messages.
PR and marketing are ONE.

Marketing and PR should work close to each other.
I would not say that PR should work totally independently from marketing, however the ways PR work is different than marketing, therefore it should be done in different way, but following the big picture made by marketing.

Public Relations is the art of building a rapport or image with the public.
As some others have already said that makes it essential that the department work closely with marketing.
One of the key points in marketing is promotion.
Public relations is a specialized core unit within a company that more intricately deals with promotion.
Working together would ensure that both departments are aligned with corporate strategy.

PR works together with marketing in same goal - build a good reputation and increase sales.
Marketing "working" with ads while PR mostly use non-paying "tools" to achive goal.
Different but work closely            

PR means that the foundation of network (Good will) with the target audience, whom are the central resource of organization’s growth.
If organization has enhanced PR in the market, the target people will not see the products’ features.
They will see who will deliver the product.

PR the front player , When he work and make the road clear , he make it easy to the Marketing player ...

Public relations is characterized as a key area important management in all institutions, and not random management or come by the institution as a response for a particular event, and it is not its task management as well as the defense of the institution errors or to lie and mislead the public. It is the management is working on dealing with the public and managed by the foundations of scientific thought and methods, so that not all people improves the practice of the profession, which seeks to influence the public through the establishment of relations of communication, bridges of trust with the public.

I think PR is not driven with the objective of making money, it has bigger motive toward creating world of mouth and serving the community

however Marketing is more driven towards market share, NOS and ensuring your ahead of competition

Yeah exactly ! Why should PR and Marketing work independently ? They are best when they are in tandem and most of the times it is the case - lest we dont realise it.

le marketing ne peut pas mener de campagne efficaces ,independamment du niveau de sophistication.