I used a laptop with the cheap interface connected to play a test file, and ran TRS cables from the line outputs of the cheap interface into the line inputs of the MOTU 16A (hooked up to a separate computer).
And when I capture the output of the cheap interface twice (same exact test file), the two recordings phase/flange when lined up and played together. When I invert the phase of one of the files, they come close to nulling for a second or two, then drift away and don't null at all, then it sometimes drifts back and almost nulls again.
When I compare the playback capture file from the cheap interface to the original test file, it also phases and flanges.
When I capture the line outputs of the MOTU 16A in the same manner, the two files almost null and don't drift around and phase/flange like the two files from the cheap interface outputs.
And when I compare the capture of the MOTU 16A to the original test file, it's almost nulls without any phasing/flanging. Even 5 passes through the MOTU DAC almost nulls with the original test file.
Apologies, hopefully I'm being clear.