I've heard some rumours that if one acquires backlinks too fast this will look unnatural too Google and they will actually lower your websites value and your SERP.

Is this true? Has anybody experienced this?

It all depends on the type of back links that you are getting. If you are getting thousands of links from free directories then it could harm your SEO efforts.

In general, Google does not punish websites for having a lot of links pointing to them. This is simply because you don't have control on who links back to you. If this was true you could simply downgrade your competitors sites by creating a lot of bad backlinks to them.

Geting a lot of crappy backlinks, will simply not do a lot for you and it's not worth the effort. Also if you EXCHANGE links with crappy sites, the link from your site might downgrade the page.

It depends on where your backlinks comes from and how did you get those backlinks. if you get those backlinks using robots and your have backlinks on a spam sites, untructed sites etc then it will definitely hurt your search engine ranking.

You probably won't get penalized but you also probably won't see your search engine rankings increase all that much either.

The more informative and relevant the site that links to yours is, the higher your own search engine ranking will become.