This isn't "more evidence can be bad", but "seemingly-stronger evidence can be weaker". If you do the math right, more evidence will make you more likely to get the right answer. If more evidence lowers your conviction rate, then your conviction rate was too high.

Briefly, I think what's going on is that a 'yes' presents N bits of evidence for 'guilty', and M bits of evidence for 'the process is biased', where M>N. The probability of bias is initially low, but lots of yeses make it shoot up. So you have four hypotheses (bias yes/no cross guilty yes/no), the two bias ones dominate, and their relative odds are the same as when you started.