I'm basing my advice from the S7 pictures.
It's going to be a little more involved than the above advice.
1) We have no idea how good the thermally conductive tape is. Here is a datasheet for the 3M product:
https://www.adafruit.com/datasheets/3m8810.PDFa) Notice that the thermal impedance goes linearly with the tape thickness.
b) The thinner the tape the less shear force it can tolerate.
2) Here are your options:
a) Send the board back.
b) Attach the heat sink yourself:
i) If you choose to do it yourself, make sure that the chip surface and cooling fin surface are perfectly clean. The cooling fin and chip surface must be in complete and uniform contact. Use isopropyl alcohol to get rid of any finger grease and dry with a clean tissue (the ones they sell to clean glasses are fine).
ii) Make sure the fins are in line with the neighboring fins as to not obstruct the air flow.
The tricky part of this option is what kind of thermal tape to use. The most conservative option is to use the thinnest 3M thermal transfer tape and keep this board under observation to see if the cooling fin stays put.
c) Disable the offending chip.
You need some super electronics expert for this step. If they could figure out if there is a resistor that could be removed that would power down/disable the chip, this would be the fastest and best.
My concern with step b) are the reports of boards burning up because of detached cooling fins.