So if you check output_log in the Enter The Guingeon/EtG_Data folder, it tells you about items you picked up from chests. Examples:
target quality: C for chest with tier shift 0 returning item Sailgun #38 of 48|C
target quality: D for chest with tier shift -1 returning item Mailbox_Gun #4 of 27|D
The 'target quality' seems to refer to which pool of items to draw from - COMMON, D,C,B,A,S. Clearly relates to chest color (brown normally gets D, blue C, green B, etc.) I just completed a run where I picked up some curse, and noticed a fair number of 'tier shift -1's in the log, while my uncursed runs never had this.
So... I think curse can cause chests to drop worse items, but we need more data. Check your output_log files for "tier shift", while doing cursed and uncursed runs, and report findings.