FWIW, I was just through DMK a few weeks back and used my ABTC card. They stamped for 30 days (presumably tourist visa - it looks like H.30? and the expiry was 30 days out).
I think it is important that we separate the two facts - for my US-issued ABTC, I used it for the ability to use the diplomatic lane, but for visa purposes, relied on the tourist visa-free exception. While I appreciate that the stated use of ABTC is for business-only. this is one of the many times that immigration seemed fine to allow use of ABTC while traveling for leisure.
They are probably within their right to turn ABTC holders away if you don't have a business visa, but I have yet to experience that myself (and I don't think I've seen a story to that effect here).