You need to try to recalculate the statistical values of your data as you can see below:
For example, under Load Min/Max values, select Min/Max, then select Actual (slower) and full/current extent depending your data, then press Load.
After computing the Min/Max values of the pixels, click apply and see if the values were updated or not.
There is nothing wrong in your data. Here is the output:
The sample raster image is your original image, and the Result raster (the one displayed) is the output after adding a value of 1.
I did not do anything exceptional, I stretched your data to Min/Max, Actual(solwer) as I explained earlier, then pressed Load. Then I used raster calculator to add value of 1 to the sample image:
"sample_raster@1" + 1
Then saved the output image as Geotiff. I repeated the above steps again of stretching the Result image to Min/Max, Actual(solwer), and pressed Load again.
That's all what I did.
I used QGIS 2.14.5. Try to update your QGIS version if you are using an older version.