No! The 1st gen FC model had the label on the back just like the 2nd gen SC and CC models. If the unit has no label on the back, then it is NOT an Intel Compute Stick product. Further, the BIOS always identified the stick as being an Intel product; it did not, for example, say "American Megatrends".
There were a number of ODMs/OEMs that copied the Intel design and put out competing products - many of which looked almost exactly like the Intel products. Here are some examples: