It is not normal for "anyone to use images like that" and I would strongly suspect that the stock photo sites either:
- have a special license option for high-traffic blogs that trades images for the plug and link; or
- those three sites have worked out a special deal with the respective stock photo houses and get free access to a limited number of images in return for the backlinks; or.
- they just pay to license the image and refer back to the stock repository because they're good people.
The only way to know for sure is to contact someone and ask.
Generally speaking you need to find Creative Commons or similarly open-licensed images or be allowed by the image rights holder before you can post them on your site with or without attribution. In some cases you can have a limited safe harbor via the Fair Use doctrine but that probably wouldn't cover you if your use was commercial or promotional in nature.^
^ I am not a lawyer nor do I play one on the internet. Consult a real lawyer before making free with someone else's work unless they clearly grant permission.