I have to post as an answer rather than a comment. I also cannot find percent min / max clip fields in ArcObjects, however they are present in the XML obtained by serializing the layer's RasterRenderer.
Here's the code to serialize, for anyone interested (straight from ESRI snippets)
IWorkspaceFactory wf = new RasterWorkspaceFactory();
IWorkspace wsrd = wf.OpenFromFile(@"\\calcium\Data\Rasters", 0);
IRasterDataset rd = ((IRasterWorkspace)wsrd).OpenRasterDataset(@"po_908238_bgrn_0000000.tif");
RasterLayerClass rl = new RasterLayerClass();
IRasterRenderer rr = rl.Renderer;
IFile xmlFile = new FileStreamClass();
IXMLSerialize mySerializeData = (IXMLSerialize)rr;
IXMLWriter myXmlWriter = new XMLWriterClass();
IXMLSerializer myXmlSerializer = new XMLSerializerClass();
myXmlSerializer.WriteObject(myXmlWriter, null, null, null, null, mySerializeData);
In my testing, a layer symbolized as shown in the picture "is" an RasterRGBRenderer, which is exclusive to IRasterStretchMinMax, so I don't think they're hiding in there.
As an alternative to serial/de-serializing, ESRI provide a StretchFunction as a subclass of IRasterFunction, which does provide direct access to clip params, although unfortunately not linked to the UI shown above.