Q:

How are GPL-compatible licenses like MIT usable in GPL programs without being subject to the copyleft provision?

I'm currently examining the possibilities and implications of linking against a GPL library for an application in a commercial context.
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).
What I don't understand is the following point from the FAQ :
If a library is released under the GPL (not the LGPL), does that mean that any software which uses it has to be under the GPL or a GPL-compatible license? 
Yes, because the software as it is actually run includes the library.
If I take a look at the GPL-compatible licenses, some of them (like the boost one) don't seem to impose the release of the code. Using it would create a situation where you could be compliant with the GPL licence without having to respect its obligation of making your code public (which doesn't seem very credible).
(NB : there are components in Adobe Photoshop licensed under boost and I don't think the code is available on demand)
The most reasonable explication would be that I'm missing something... Could you please tell me where I made a mistake ?

A:

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.
Long answer:
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).

[emphasis added]
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 Foo.
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 or Bar+Foo, is still available under the Boost license.  Said another way, Bar+Foo has no license impact upon Foo itself.
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+Foo, delete 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.

A:

By "GPL-compatible", they mean, a license that does not conflict with the GPL.  A less restrictive license, like the Boost license, is "compatible" with the GPL because it doesn't restrict users of the code from doing anything that the GPL would allow a user to do.  That is, the Boost license allows people to copy freely, which is what the GPL requires people are allowed.
An example of a license that is not "compatible" would be a license that required a fee to the original authors for users to distribute copies.  Since the GPL explicitly permits both free and paid distribution, this more restrictive license would not be compatible.
In other words, the GPL says "You must allow $A, $B and $C".  Any license that allows $A, $B, $C and also $D and $E is compatible.  A license that allowed $A and $B but not $C would not be. 

