The image below can be obtained by adding WorldTimeZone layers to the JSAPI map:
wmtsLayer = new esri.layers.WMTSLayer("http://servicesbeta4.esri.com/arcgis/rest/services/WorldTimeZones/MapServer/WMTS", options);
tiledLayer = new esri.layers.ArcGISTiledMapServiceLayer("http://servicesbeta4.esri.com/arcgis/rest/services/WorldTimeZones/MapServer", { opacity: 0.5});
I believe this issue is that the WMTS scale values are based on 0.28mm/pixel instead of 96 DPI.

Is there a way to make these two layers align correctly?
Because a proxy is required I cannot provide working source but I did paste my code here.

