Yep, the quality of transport does make a difference.
I had one of original (well respected for the money) Oppo universal players. Upgrading to an Onix CD-3 added bass body and overall resolution. Computer transports are better yet. And just to confuse some more, you can add a music server to your computer, like a Logitech Duet or Touch for instance which has digital and analog outputs. The digital output section is also called a transport. And check out the Bolder Cable circle where Wayne mods the digital (transport) only.
One of major factors of playback for transports is called jitter which relates to the deviation in or displacement of some aspect of the pulses in a high-frequency digital signal as it is pulled off the disc and transmitted (yes even the digital transfer mode). Jitter has been blamed for much of what is termed "digital" sound and the industry has been trying to conquer it for nearly 30 years.
Sorry, no free (or cheap) lunches.