So Pixieset shrinks the pixel dimensions of your files, AND re-compresses them - really aggressively.
I've done some file comparison in the past, and even though you can see, when you examine really close, that the Pixieset files are degraded in quality, it's not enough degradation to actually make a difference to the print quality. You may rest assured of that.
However, it's DAMNED hard to convince a client like yours that their smaller files will print fine. Clients are funny like that.