Dude. Those numbers are backwards.
Look at it this way. On average, each person has 2,000 billable hours per year (40hrs/week * 50 workweeks/year = 2,000 workhours/year). So therefore, if you want to make $50k this year (gross, pre tax) you can charge $25/hr ($25*2,000=$50,000). To earn 6 figures you need to charge at least $50/hr.
Those numbers are correct. If you've worked at freelancing for a half a year, you will realise that
1) It's not possible to push 40 hour weeks freelancing.
2) Your work year will not have 50 weeks.
Now, clients want to get charged by the hour on the actual programming stuff you do. However, there is also
1) Initial communication
2) Help with creating the spec
3) Additional communication during the project development
4) Time wasted at the end of the project.
If you're working freelancing, you'll know how important it is to get a new client BEFORE the current project ends, otherwise you will be back to living in your parent's basement.
So you're going to waste time with potential clients who are just shopping around and wasting everyone's time. You are going to waste time analyzing specs and giving quotes to clients who go and hire someone else. At the start when you need all the clients you can get, you'll even waste time writing specs for clients who will take them to other programmers.
Unless you are working from an office you rent, you will have an infinite number of distractions. If you have a girlfriend, wife, kids, you're fucked. If you're working from home, you will have discipline issues, you'll find it hard to wake up at proper times and start working like a good ass employee, and work done late at night will be sloppy - life isn't quite as easy working for someone else who have detailed specifications as it is when working for yourself. Since you have no management overlooking you, several hours per day will be wasted at forums like wickedfire, browsing coder blogs, etc.
Take away from that vacation money and time you don't get, insurance, taxes, additional perks, computers, software, etc.
Basically, you waste SO much fucking time and money you have to charge much much more. That being said, 4x is a bit of an exaggeration.