How are GPL-compatible licenses like MIT usable in GPL programs without being subject to the copyleft provision?
Short answer: They're not. They'll become subject to the copyleft.
The Wikipedia article on license compatibility has a good section on GPL compatibility:
Many of the most common free software licenses, such as the original MIT/X license, ... are "GPL-compatible". That is, their code can be combined with a program under the GPL without conflict (the new combination would have the GPL applied to the whole).
And more explicitly from the FSF FAQ on GPL compatibility:
It means that the other license and the GNU GPL are compatible; you can combine code released under the other license with code released under the GNU GPL in one larger program.
And just for edification, here's the FSF's comments on various licenses
FSF's comment on the boost license
This is a lax, permissive non-copyleft free software license, compatible with the GNU GPL.
Which means that anything licensed under Boost is easily subsumed by the GPL.
Where it gets tricky
Let's say we have project
Foo licensed under Boost, and project
Bar licensed under GPL and which wants to use
Bar+Foo is allowed since the licenses are compatible, and the release of
Bar+Foo must be GPL as
Bar is GPL.
Foo, by itself and without
Bar+Foo, is still available under the Boost license. Said another way,
Bar+Foo has no license impact upon
The resulting license of the project combination is a forward acting event for the combination only. It is not a retroactive event.
So if someone else wants to take
Foo and do something else with it, they are still free to do so without the copyleft provision of the GPL. However, if they take
Bar and only use
+Foo then they are still bound by the terms of the GPL since
Bar+Foo was GPL'd.
Your other question:
From what I've understood of the GPL, as long as the application is used internally there is no obligation to release its code (even if a copy is moved to a controlled subsidiary).
This is directly answered by the FSF GPL FAQ on source distribution
The GPL does not require you to release your modified version, or any part of it. You are free to make modifications and use them privately, without ever releasing them. This applies to organizations (including companies), too; an organization can make a modified version and use it internally without ever releasing it outside the organization.
Wholly owned subsidiaries are considered part of the parent organization, so you would legally be in the clear. FSF would point out that you are violating the spirit of Free Software though.