64-bit Windows guest in VirtualBox impossible without VT-x support?

Section 3.1.2 of the VirtualBox manual explicitly states that you need hardware virtualization support to use 64-bit guest operating systems (emphasis added):

VirtualBox supports 64-bit guest operating systems, even on 32-bit host operating systems, provided that the following conditions are met:

  1. You need a 64-bit processor with hardware virtualization support (see Section 10.3, “Hardware vs. software virtualization”).

  2. You must enable hardware virtualization for the particular VM for which you want 64-bit support; software virtualization is not supported for 64-bit VMs.

  3. If you want to use 64-bit guest support on a 32-bit host operating system, you must also select a 64-bit operating system for the particular VM. Since supporting 64 bits on 32-bit hosts incurs additional overhead, VirtualBox only enables this support upon explicit request.

Source: https://www.virtualbox.org/manual/ch03.html#intro-64bitguests

Section 10.3 also states this (emphasis added):

VirtualBox's 64-bit guest support (added with version 2.0) and multiprocessing (SMP, added with version 3.0) both require hardware virtualization to be enabled. (This is not much of a limitation since the vast majority of today's 64-bit and multicore CPUs ship with hardware virtualization anyway; the exceptions to this rule are e.g. older Intel Celeron and AMD Opteron CPUs.)

Source: https://www.virtualbox.org/manual/ch10.html#hwvirt

Thus, you need a processor that supports VT-x or AMD-V to use 64-bit guests with VirtualBox. However, QEMU, Bochs and VMWare Player all support 64-bit guests without hardware virtualization support (at least according to this page).