I don't think that is the case. See Red Hat's statement on that Cygwin page:
"As a special exception to GPLv3+, Red Hat grants you permission to link software whose sources are distributed under a license that satisfies the Open Source Definition with libcygwin.a, without libcygwin.a itself causing the resulting program to be covered by GPLv3+."
OO is licensed using Apache SL2. I haven't checked very recently, but that likely satisfies the OSI open source definition.
Historically, usage of Cygwin, which has been extensive, and long (I've been advocating it and helping people with it since 2001, at least, and that includes some OO work) has not caused license panic. Red Hat seems intent on ensuring that calm prevails and that people use it freely and regularly without having that heart stopping moment of regret that would turn them to something else.
Cygwin is used only for building Windows binaries. The resulting binaries
are native Windows and neither use nor distribute the Cygwin DLL.
(The Visual Studio VC++ tool chain is run from within the CygWin shell, and
that is what provides the completely-native Windows binary for Apache
OpenOffice. If you use the same build process, that will be the case for
your builds with respect to Cygwin.)
If your built binaries incorporate essential dependencies on third-party
libraries, you must respect the license requirements on those libraries, as
well as the Apache License version 2.0 (and other licenses) on the Apache
OpenOffice source code.