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The signal can get really distorted. The cables need to be shielded or use twisted pair construction to reduce noise, and they all have to be the same length to avoid timing issues, as well as be the correct impedance. Any cable that meets HDMI specifications has those things, and will work equally well. A HDMI connector soldered onto some random wire you found on your workbench will not work equally well. The "It's digital, so signal quality doesn't matter" statement is untrue, but the purpose it serves (to dissuade people from choosing obscenely overpriced cables) is valid.
It's simple enough to provide many other instances where digital signal quality matters. Why do you use Cat6 for gigabit, when Cat5 has the same number of wires? The signal either gets there it it doesn't, right? Except Ethernet needs twisted pairs to reduce outside interference, the different pairs are twisted at different intervals to reduce crosstalk, and they need to be twisted right up to the connector. Again, a $1 ethernet cable has the correct construction to meet the gigabit standards, and Monster likely sells a $100 ethernet cable that is not any better. But again, crimp an ethernet connector onto a mishmash of spare wires, and it will not work right.