I believe there is some confusion here, as there is a difference between I/O and non-I/O devices.
From wikipedia Memory-mapped I/O (MMIO) :
uses the same address bus to address both memory and I/O devices – the
memory and registers of the I/O devices are mapped to (associated
with) address values. So when an address is accessed by the CPU, it
may refer to a portion of physical RAM, but it can also refer to
memory of the I/O device. Thus, the CPU instructions used to access
the memory can also be used for accessing devices. Each I/O device
monitors the CPU's address bus and responds to any CPU access of an
address assigned to that device, connecting the data bus to the
desired device's hardware register. To accommodate the I/O devices,
areas of the addresses used by the CPU must be reserved for I/O and
must not be available for normal physical memory.
From your article :
Base address Registers (or BARs) can be used to hold memory addresses
used by the device, or offsets for port addresses. Typically, memory
address BARs need to be located in physical ram while I/O space
BARs can reside at any memory address (even beyond physical memory).
The Type field of the Memory Space BAR Layout specifies the size of
the base register and where in memory it can be mapped. If it has a
value of 0x00 then the base register is 32-bits wide and can be mapped
anywhere in the 32-bit Memory Space. A value of 0x02 means the base
register is 64-bits wide and can be mapped anywhere in the 64-bit
Memory Space (A 64-bit base address register consumes 2 of the base
address registers available).
Thus there is no conflict between the two, as it all depends on the device.
If the device intercepts the memory reference on the bus, then the address is virtual.
If it doesn't, then it's real physical address that is used to communicate with the device
(for example NVRAM).
However, in all cases, real physical address is used for I/O devices, since computer instructions that refer to it can only use real addresses.
This memory may be wasted if the device intercepts references to it.
To avoid such waste, the operating system will usually allocate it beyond the
real physical memory (this will cause no errors of bad memory access,
since the device will intercept all references).
This is the reason for the well-known problem of 32-bit Windows computers
not seemingly being able to use the entire 4 GB of memory.
The reason was that Windows, being 32-bit, allocated device memory using real addresses,
which then became unavailable for both the cases:
whether the addressed memory was really used,
or unused because intercepted by the device.
Another useful wikipedia article is : PCI configuration space.