Goatwuss, Stingreen and Tricon_dave are correct. This LP plays fine in my system too but I have two friends with (less capable) systems which distort it just as you described, especially the inner tracks.
We've played the same copy in all three systems. Only in mine is it listenable (assuming one applies such a term to Allison Krauss). ;-)
It's a challenge not only for a cartridge/tonearm, it's a major challenge for a phono stage. The recording was miked closely, fundamentals and harmonics are quite close together and amplitudes are high. These factors challenge each component's ability to avoid sibilance (due to intermodulation between powerful, closely related waveforms) and crackling (due to physical mistracking, phono stage overload or both). The more tightly packed modulations of an inner groove just compound these challenges.
This record's a pretty good demo for a good system, or a pretty stiff challenge for one that's still developing.