The usual configuration is to take the Dolby Digital AC-3 stream from SPDIF *output* of a DVD player, and use it to drive the SPDIF *input* of either a standalone Dolby 5.1 decoder or an integrated HT receiver.
The Dolby Digital decoder circuitry inside most DVD players doesn't usually decode the Dolby Digital AC-3 over SPDIF input internally. Typically, it's a multichannel DAC that's driven by the microcontroller directly, either over I2S or some other proprietary interface that carries the AC-3 stream.
It isn't that easy to take an AC-3 stream over SPDIF and use it to drive the internal Dolby decoder of a DVD player, though their are some codec chips that do have an SPDIF input with this capability, e.g. Realtek ALC888 or similar (typically used on PC motherboards).