Think of Penguin as being more about spam.
With regard to backlinks... for some, that line gets a little fuzzy. Freely given editorial links, even when you "beg" for them, are OK. If you begged so hard that you were given 10,000 run-of-site links all with the same anchor text, then they no longer appear to be either "freely given" or "editorial" to Google.
Intent plays a big part in it. Building profile links from irrelevant sites for the sake of directing PageRank to your site, eg, is easy to spot, and the intent is generally quite clear. So is hiding links in sponsored WordPress themes. Yes, it can be hard to recover from Penguin.