Id be interested in hearing where your friend learned that from as there is little reference to anything between the ships in particular that speaks to it. And several factors against such a possibility.

The main one is that the ships simply id not serve in each others company very long. Zuikaku was only placed in commission at the end of September 1941, and was then immediately thrown into the strength of Kido Butai for the Pearl Harbor operation. Following that the 6 carriers generally did act in company aiding Japanese conquests in the Dutch East Indies.

However Kaga had run aground in February 1942 and in mid March had to go back home for repairs. That meant that she missed the India Ocean Raid in April. After that the 5th Carrier Division with Zuikaku was immediately sent to Truk to then support the MO Operation that would lead to the Battle of the Coral Sea, while the other carriers returned to the Home Islands for a frenzied period of preperation for the MI Operation and their meeting with fate with Kaga taking her place in Carrier Division 1 with Akagi.

So all told the 2 carriers were in each other's company for for only about 5 months and even then did not directly operate together for portions of it.

What this might be in reference to is the low opinion that the 1st and 2nd Carrier Divisions held the 5th in. As the new comers the Shokaku and Zuikaku were thought of as the amateur hour portion of the Kido Butai. And that anything they could do the veterans on the other 4 carriers could match or best.