On Open Source Initiative website you can get an explicite answer to your question. This website have list of all opensource licences including GNU GPLv3 :
Can Open Source software be used for commercial purposes?
Absolutely. All Open Source software can be used for commercial purpose; the Open Source Definition guarantees this. You can even sell Open Source software.
However, note that commercial is not the same as proprietary. If you receive software under an Open Source license, you can always use that software for commercial purposes, but that doesn't always mean you can place further restrictions on people who receive the software from you. In particular, copyleft-style Open Source licenses require that, in at least some cases, when you distribute the software, you must do so under the same license you received it under.
So for part, To my understanding software under GPLv3 can be used commercially (e.g. as tool for company-internal calculations) with no restriction.
You are correct software under GPLv3 can be used commercially with no restriction. But in that case your developed code must also be under GPLv3 and this is the restriction imposed so that no middlemen could strip off the freedom.
Intention is clear in What Is Copyleft? section.
The simplest way to make a program free is to put it in the public domain, uncopyrighted. This allows people to share the program and their improvements, if they are so minded. But it also allows uncooperative people to convert the program into proprietary software. They can make changes, many or few, and distribute the result as a proprietary product. People who receive the program in that modified form do not have the freedom that the original author gave them; the middleman has stripped it away.
In the GNU project, our aim is to give all users the freedom to redistribute and change GNU software. If middlemen could strip off the freedom, we might have many users, but those users would not have freedom. So instead of putting GNU software in the public domain, we “copyleft” it. Copyleft says that anyone who redistributes the software, with or without changes, must pass along the freedom to further copy and change it. Copyleft guarantees that every user has freedom.
Further:
To copyleft a program, we first state that it is copyrighted; then we add distribution terms, which are a legal instrument that gives everyone the rights to use, modify, and redistribute the program's code or any program derived from it but only if the distribution terms are unchanged. Thus, the code and the freedoms become legally inseparable.
That mean, if you are using GPLv3 licenced software then your developed application is also abide by GPLv3 and you need to share your source code with your client i.e. by putting it in public domain, share a copy of code with software etc.
Here comes the For a commercial usage/redistribution, please contact XXX to obtain a commercial license. part of the README. Offten, venders choose not to share their source code but wants to use the softwares which are available under GPLv3 licences. In that case, vendors evaluate the software and if it fits to their need then they ask for non-GPL licence from the origional software provider if the software provider have this option ( which is in this case).
