I've been staying out of this - actually waiting to see what Peter G. has to say.
I can't help with what Ueshiba exactly said but since you mention kanji - from the Shodokan FAQ
It is often argued that Aikido is "The Budo of Love" and therefore there shouldn't be any form of competition in Aikido. This argument is a good one and arises from the very important Aikido and Budo concept that fighting and aggression are wrong.
We do not think of Shiai (competition) as aggression or fighting against an opponent. If we really think about it the (Japanese Kanji) word 'Shiai' (competition) is made up of two parts. The first part 'Shi' means to test and the second part 'Ai' means together with someone.
Thus we view Shiai as a valuable opportunity to test ourselves whilst working together, and as a useful aid for studying our 'Waza' (art) and our 'Do' (way).
Originally posted by akiy
I'm wondering because the word "competition" can be translated as both "shiai" as in a judo tournament kind of competition or "arasoiai" which can mean stuff like rivalry, non-physical fighting, and such.