Is my DAC the Marantz or the Oppo?

I have a USB drive of FLAC files, and two ways of playing them. I want to pick the best method for quality playback, which I believe is using my Marantz AV7005 Pre/Pro as the DAC.

METHOD 1: Plug the USB drive into the front panel of the Marantz AV7005, and use its interface to navigate the drive and play the FLACs. Obviously the Marantz acts as the DAC here.

METHOD 2: Plug the USB drive into an Oppo BDP-93, which is connected to the Marantz with an HDMI cable.

For method #2, is the Oppo or the Marantz acting as the DAC? Another way to ask this question is this way; Does the HDMI cable that connects the Oppo to the Marantz send 1's and 0's to the Marantz for decoding, or, does the chip in the Oppo come into play before sending actual "sound" to the Marantz?

If I were to guess, I'd say that HDMI cable can only send a digital signal by design, and in either of my configurations.... the Marantz is the DAC.

I ask because I kind of like the Oppo's interface a little better. And the corresponding IOS app, too. It just looks a bit slicker with album artwork, etc. But I have to think that I want the more expensive Marantz to be doing the work for me. Please keep in mind that this Oppo Blu-ray player is not the advanced model with balanced outs that can hook up directly to an amp.... it is HDMI-only in my system.

So what do you say? Does feeding my Marantz FLACs from an HDMI cable take the burden of processing off my Marantz (which I don't think I want), or does the Marantz Pre/Pro remain the DAC whether the USB drive is directly connected or indirectly connected (over HDMI)?

Thanks !!!