It is not your fault and, of course, it is not your responsibility. Keep HTTP status codes, they are useful. If some of your users decide to install a browser plugin that processes 404 status codes, do not try to bypass it.
This blog has a Google Webmaster Central blog entry :
[...] confusing for users, and in addition, search engines can spend most of their time crawling and indexing non-existent, often duplicate URLs on your site. This can adversely affect your siteβs crawl reach - due to the time Googlebot spends on non-existent pages, your unique URLs cannot be detected as quickly or frequently visited.