There seems to be a mix of different topics here:
1. Bitperfect reproduction
2. Streaming of dts files
3. Correct reproduction of dts files
1. is possible in foobar through WASAPI or ASIO, it only depends on
the selected output.
2. streaming is NOT possible through foobar out of the box, afaik.
foobar will instead decode to PCM and pass the decoded signal to the
receiver (Receiver will not light up because the internal codec is not
used). There are a few workarounds like a SPDIF output plugin which
work for some but not for others, depending on the hardware and OS
used.
3. Basically, Windows has an inbuilt limitation for dts files.
Usually, they can only be reproduced as 48khz, even if they're 96khz
(The 96khz part would be used for a very small frequency range anyway.
foobar will reproduce dts files in a variety of ways which can be
changed by simply changing the file extension.
4. The case of wav-dts is a special case and is often misunderstood
since WAV can refer to either a file format or a container format. In
the case of WAVDTS, dts is simply embedded in a wav-container but is
still lossless. When converting these files to FLAC, a lossless file
format, one transcoding effectively from lossy to lossless. This
should be avoided at all costs, because people usually don't keep a
history of their files and will finally "sell" those files as
genuinely lossless to others.
Sorry for ranting, please do point out if there are errors in my
statements.