Why do faulty headphones make MP3s sound low bitrate when I touch the wire?
Perhaps it sounds like a low bitrate because that is the perceptual degradation that you are most familiar with and therefore associate with the new form of degradation.



One of the major floors of the TRS(/TRRS) design is that the connections are placed on one pin (as opposed to e.g. XLR where the connections are on separate pins). This means that the TRS contacts can connect with the wrong contacts inside the female connector, creating odd sounding results. 

Potentially what could have happened is that you have bridged two connectors which is causing left and right to be summed into one side of your headphones, which can cause phase and impedance issues. Other combinations of connections could cause a variety of weird issues when you throw a microphone connection into the mix.