This is from Wikipedia:
The overall reaction has its limits. Overdischarge supersaturates lithium cobalt oxide, leading to the production of lithium oxide,[36] possibly by the following irreversible reaction...
Seems to me that it could be possible to have local supersaturation with a high initial discharge rate - I have heard of 'forming charge' - maybe that is setting up the anode/cathode chemicals so they saturate evenly?
Unfortunately, organic solvents easily decompose on anodes during charging. However, when appropriate organic solvents are used as the electrolyte, the solvent decomposes on initial charging and forms a solid layer called the solid electrolyte interphase (SEI),[41] which is electrically insulating yet provides sufficient ionic conductivity. The interphase prevents decomposition of the electrolyte after the second charge
Similarly, the lithium batteries are relying on chemical changes within the cells. I would believe that a rapid discharge could be harmful if this initial chemical 'shield' was not fully developed on the first charge, or the first 5 charges, and thus would prefer a few break-in cycles to complete the necessary reactions.
I take Wikipedia with a grain of salt. However, chemical reactions to take time, and I could easily believe that the necessary chemical changes in a lithium battery are not fully developed after the first cycle.