Stanley Porter and Buist Fanning as well as K. L. McKay have drawn our attention to aspect morphology and its relationship to ancient Greek. Maximilian Zerwick also has this to say about "tense" (TEMPUS) in Biblical Greek:
"The 'future' and the 'present' do connote time so far as the name is concerned, but not even the names of the other 'tenses' express the notion of time: the name 'imperfect' connotes incompleted action and 'perfect' completed, while 'aorist' (privative A and hORIZW 'define, determine') connotes simply the action without further determination. Hence the very names of the 'tenses' warn us to distinguish carefully between the notion of the time of an action and of the manner in which the action is regarded, its 'aspect'. In fact, 'aspect' is an essential element of the Greek 'tenses' (leaving out of account the future) and hence is always distinguished by the form, whereas the time of actions is expressed in the indicative only, and in the other moods is either lacking or secondary" (Zerwick, Biblical Greek Illustrated by Examples, p. 77. Inverted commas in original).
Yet Richard Young states: "There is good support for the contention that the morphological features associated with Greek tense indicate only aspect, not time, and that time is established by the context rather than grammatical form (cf. Porter 1989:76-83; McKay 1981:290, 296). If this contention is correct, then it would be misleading to retain the term 'tense'" (Intermediate NT Greek, 105). The examples that he gives are John 1:29 (past reference time), Acts 16:18 (present reference time), Luke 19:8 (future reference time), and John 3:18 (timeless reference).
I'm not saying that time is not grammaticalized in Greek, but I do believe that Greek tenses and moods function much differently from English or Latin tenses/moods. So do the sequence of tenses/moods. At any rate, it appears that tensed Greek are not as rigid as those in Latin.