Even though the "chiefs" clearly refer to the Istari, I would not make much of it. If one wanted to maintain that wording at all cost and reconcile its meaning with the other texts, one might apply it instead to "the Wise" which are defined as "the chieftains of the Eldar and the Istari" (HoME XII 1, viii) and "the Istari and the chief Eldar" (app. B) in the published version.
Taking into consideration that to most, the nature of the Istari was not clear, and that they were commonly mistaken for Elves (at least among men) might show how the lines could have been blurred here. Tolkien himself briefly and hesitatingly wondered whether Glorfindel was a wizard (cf. HoME 2, xiii).
In this case, however, even though it appears that Tolkien maybe even deliberately kept the true number of Istari a relative secret, throughout The Lord of the Rings at any rate, the answer which can be derived from the background writings is definite. In his Letters, Tolkien never questions the number of five when he gives it, but in his Last Writings, he brought it all together by stating both points we have been working on: "Saruman in his wrath mentioning five [Istari] was letting out a piece of private information" (ibid.). The existance of the blue wizards was actually only known to the other three (ibid.).
This says both that the number was hard, if not impossible to tell for outsiders, because it was intentionally kept hidden (from Sauron), and that there very clearly were five.
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