You don't want to match impedances, you want to bridge them. Thus the recommendation to have 10x input impedance as the output impedance of your guitar.
Matching impedances maximizes power transfer, but you don't particularly care about powering the line input. You want to transfer voltage, and to minimize the voltage drop, ideally you want a much higher input impedance.
If you take a simple case of a non-reactive source, then if you match impedances you will lose half your signal to impedance of the source. But guitars aren't non-reactive sources, so the signal loss is not uniform. A guitar pickup is an inductive source, so it will form a basic low-pass filter with the input impedance of the card. The lower the input impedance, the lower the corner frequency of the filter. You want a high input impedance to get that corner way high out of the audio band.
Why haven't you heard a difference using a DI? Two possibilities I can think of offhand: first, you may be using an instrument with active pickups. In that case, the output impedance is much lower than 10K ohms, so you have no problem.
Second, it's possible the DI you are using also has an inappropriately low input impedance, so the signal degradation occurs whether you run through it or not. This may be the case with inexpensive cable-connector type impedance converters.
