The BDA-3 does reclock the signal, though I don't know the details.
But with these types of connections, the master clock is still in the source. The DAC has to recover the clock. In the old days this used to be via a phase locked loop. There are better technologies today that are considered "reclocking", but they don't fully decouple from the source's clock. They can't, or they would risk data-under-run problems.
This may be why asynchronous USB is becoming more popular (plus the extra data rate and ability to send DSD). In that case, the master clock is in the DAC. However, I find AES/EBU has a deeper more natural soundstage, with less etched highs, in my BDA-3.