I believe what AMD is talking about and mentions "Thermal Solutions" is a proper 3rd Party or AMD CPU Cooler.
Normally the AMD CPU Coolers that comes bundled with a processor already has a pre-applied Thermal paste on it that is covered up with a clear plastic film or possibly comes with a tube of Thermal paste for the User to apply.
The CPU Cooler heat sink that sits a top of a processor is normally covered with a plastic film to prevent it from getting damaged before being installed.
AMD Warranty states you must have a CPU Cooler that is recommended for the AMD Processor. In another words, if you put a CPU Cooler that isn't strong enough to maintain the AMD processor from overheating and the processor gets damaged the warranty is voided:
This Limited Warranty shall be null and void if the AMD microprocessor which is the subject of this Limited Warranty is used with any heatsink/fan (HSF) that does not support operation of the AMD processor in conformance with AMD’s publicly available specifications. Use of HSF solutions determined by AMD as incapable of such performance or which are determined to have contributed to the failure of the processor shall invalidate the warranty.