I seriously doubt that the difference in streamers has anything to do with data integrity. I would expect that every streamer can deliver the digital information to the DAC without introducing any data errors.
But DACs are very sensitive to analog noise and timing errors on the digital data signal. Higher-end DACs put a lot of effort into minimizing these effects by using digital isolators, reclocking, PLLs, etc. but these DACs also tend to be more resolving allowing differences in streamers to be more obvious.
High-end streamers go to great pains to minimize noise and clock errors by utilizing complex data isolation and FIFO reclockers, extremely high-accuracy clocks with low jitter and phase noise, ultra-quiet power supplies (even battery or ultra-capacitor powered), high-bandwidth digital line drivers, etc. to deliver the cleanest possible signal to the DAC. This does not come cheap.
How much this affects sound quality will, of course, depend on the DAC being used, how noisy the signal to the streamer is, the cables and connection type being used, and the resolving power of the overall system.
But if I was spending $20K on a DAC, I certainly wouldn't expect to get the best out of it with a $500 streamer.