As it turns out, Toggle Chasecam is actually affecting the console variable "chasecam". When "chasecam"'s value is changed, this console variable modifies the value of the "analog" console variable (forces it to off when "chasecam" is off or "useranalog" is off; forces it on otherwise). In turn the "analog" console variable messes with "cam_dist" when changed - it's forced to be 192 for analog mode, and 128 otherwise.
In short, Toggle Chasecam modifies "chasecam" modifies "analog" modifies "cam_dist"! This is hardly the only occasion SRB2 modifies "cam_dist" though sadly.