You have to drill down a bit deeper into their site to get their actual numbers:
http://www.rescuecom.com/blog/index.php/pc/rescuecom-releases-2015-q1-computer-reliability-report/
Their methodology is not entirely unsound. Unfortunately since they don't give n (number of calls received), you can't calculate uncertainties in their figures. Statistically, the 30.7% of service calls they received for HP may actually be 30.7% +/- 20%. Meaning HP's long-term average might be 11%, but this past quarter they got extraordinarily unlucky and it spiked to 30.7% by sheer chance alone. The bigger their sample (the bigger n is), the smaller the uncertainty. But without knowing n, it's impossible to say how reliable their data is.
Squaretrade (yeah, that company that sells extended warranties when you buy a PC at Best Buy) has a more sound methodology. They track the number of insurance policies they sell for a brand or device, and compare it to the number of claims that are filed. Unfortunately, they don't put out a report every quarter like RescueCom.
https://www.squaretrade.com/warranty-buyer-knowledge-base.
In the big picture though, it doesn't really matter. HP, Apple, Dell, etc. don't actually make laptops. They're designed and manufactured by Taiwanese companies you've probably never heard of called ODMs. The name brand just slaps their label on it before selling it to you.
https://en.wikipedia.org/wiki/List_of_laptop_brands_and_manufacturers#Original_design_manufacturers_.28ODMs.29
The Macbooks are made by Quanta. Quanta also happens to make most of HP's laptops. So if you figure the Macbooks are reliable because of the manufacturer, then so too must be most of HP's laptops. Unfortunately it's almost impossible to figure out which ODM actually made a particular model laptop. So the HP you buy may be made by a sucky ODM (Wistron, which used to be the manufacturing arm of Acer in the 1990s is widely considered to have low quality), or it may be made by a good ODM. A certain Dell model may have more in common with a certain Toshiba model than it does a different Dell model. So trying to break down reliability by brand name is a fool's errand.
I believe Samsung makes their own laptops. And I think Lenovo's Thinkpad line is still made in-house. Sony's top-end model used to be made in-house as well, but then they went and sold their entire VAIO line so they're probably all ODM rebrands now.