Indeed, multiple news reports that the government has confirmed plans to introduce DST have been shelved.
> To: tz@iana.org
> From: eggert@cs.ucla.edu
> Date: Wed, 13 Jan 2016 11:38:20 -0800
> Subject: [tz] Opposition to Cayman DST
>
> Currently tzdata is guessing that Cayman will introduce daylight saving
> time this year. This is not official, though. There is opposition in the
> Legislative Assembly, and if the LA rejects it we will need to update
> tzdata.
>
> Ragoonath R. Gov’t Daylight Savings Time plans to get resistance in LA.
> Cayman Reporter 2016-01-08.
> http://www.caymanreporter.com/2016/01/08/govt-daylight-savings-time-plans-get-resistance-la/