And, here's a diagram showing that hFE is not just one value, but can be vastly different depending on operating point.
I suppose you can argue that the VCE(sat) point (red dot), is not a Beta value, because the transistor is in Saturation, but, it's still the ratio of IC to IB, which, as I understood, is the definition of Beta. So, maybe the point of contention is type of Beta. Perhaps the distinction is Active Region Beta, vs.Saturation Beta. OR, Maximum Possible Beta [those hFE specifications on the datasheet] and Forced Beta [i.e. using Beta to position the operating point on the Characteristic curve]. For switching, the goal is to get as close to the ideal switch model in a tradeoff between practicable and practical. This usually means a Beta of 10 to 20. For a, for instance, Class A amplifier, the beta will, typically be set to a higher point. But, rarely will the transistor operate at its maximum possible beta. Usually a linear amplifier design goal is to swamp out variations in beta [due to temperature changes, changes in collector current, and production variances].