They use the word "kitai", but it's not really any different from the English variant. It is merely Fukube's take that is quite unique, and I thought you were referencing that usage since you put "having expectations" in quotation marks.

When I said being "unable to do it yourself", I meant in terms of capability, not the situation. Fukube tried and failed to solve the Juumonji case, so he was forced to leave it to Oreki. He realized his own limitations. Fukube's usage is about a person's potential and ability, as shown by the scenes where his insecurity surfaces. Oreki's did not have such feelings in this episode, so him asking for help from Fukube does not fit into Fukube's definition of "expectation".