According to the biography of Otsuka by his grandson Kazutaka Otsuka...
"When he was 31 years old, he heard of Funakoshi Sensei from Okinawa living in a Meiseijuku dormitory, which was for the university students of Okinawa and he started studying at the Meiseijuku dormitory in the dining room. Funakoshi Sensei asked Grand Master Otsuka if he knew karate before because Shinto Yoshin Ryu already included striking and kicking techniques. Funakoshi Sensei knew only 15 katas at that time and Grand Master Otsuka completed those in less than one year. Then he wasn’t satisfied with only learning order of katas, so he wanted to visit Okinawa to find out about meaning of each movement, but Funakoshi Sensei denied him going to Okinawa. Funakoshi Sensei had reasons for not wanting to return to Okinawa. Because of debts incurred by Giei, his son, he was unable to return to Okinawa. Three years later, Grand Master Otsuka visited two Okinawa senseis, Mabuni Kenei and Choki Motubu who were living in Osaka City, in order to learn more detail about Okinawan karate. He asked Motobu Sensei about details of each karate techniques and they shared techniques with each other. He then asked about the actual situation of karate in Okinawa and found out there was no further information for him there, so he decided not to travel to Okinawa but to study himself about karate and jujutsu and to create a new style"
There is little evidence to support the fact that Otsuka trained extensively with Motobu, let alone the suggestion that his main reason for doing so was because of Kumite.