Wikipedia has quite a good section on this topic:
Although the OSI definition of "open source software" is widely accepted, a small number of people and organizations use the term to refer to software where the source is available for viewing, but which may not legally be modified or redistributed. Such software is more often referred to as source-available, or as shared source, a term coined by Microsoft in 2001. While in 2007 two shared source licenses were certified by the OSI, most of the shared source licenses are still source-available only.
In 2007 Michael Tiemann, president of OSI, had criticized companies such as SugarCRM for promoting their software as "open source" when in fact it did not have an OSI-approved license. In SugarCRM's case, it was because the software is so-called "badgeware" since it specified a "badge" that must be displayed in the user interface (SugarCRM has since switched to GPLv3). Another example was Scilab prior to version 5, which called itself "the open source platform for numerical computation" but had a license that forbade commercial redistribution of modified versions. Because OSI does not have a registered trademark for the term "open source", its legal ability to prevent such usage of the term is limited, but Tiemann advocates using public opinion from OSI, customers, and community members to pressure such organizations to change their license or to use a different term. Although the OSI definition of "open source software" is widely accepted, a small number of people and organizations use the term to refer to software where the source is available for viewing, but which may not legally be modified or redistributed. Such software is more often referred to as source-available, or as shared source, a term coined by Microsoft in 2001. While in 2007 two shared source licenses were certified by the OSI, most of the shared source licenses are still source-available only.
So it boils down to the fact that quite a lot of companies have actually done the thing you were wondering about and whether the term open source may be used to describe this behavior has been debated quite a lot and taking a position one way or another would make for an incomplete answer. The simple reality is that open in open source can both mean openly available and free to be changed depending on the context of where and with whom the term is used. In the source code world there is a whole range from 'public domain' down to 'closed source' and the best thing to realize is that it's best to just judge each license on its own merits.
The important thing however is that there definitely are licenses that allow you to do exactly what you want to do, regardless of how they are called. There are however no freely-usable licenses of such type that I know of, as a license - just like any intellectual work- is by default copyrighted, so companies tend to just write their own license when they wish to make their source code view-able.
