Is 23.8°C/W junction-to-ambient thermal resistance for a TO-220 in this datasheet with or without a heatsink?
It seems to me that TI is being far more detailed in their description and measurement for this particular component than the other manufacturers and other components by TI.

Datasheet

First of all, ignore everything that specifies a copper area - that's for SMD packages and does not apply to TO-220 packages unless you treat them like some ghetto TO-263 package. The intended way for heat to flow out of a TO-220 is through the tab into ambient air or a heat sink.

Second, it can't possibly be the value for a heat sink. If so, it would be a tiny heat sink, and more importantly, the heat sink would have to be specified.

Section 6.1 and 6.3 as you say mentions "All numbers apply for packages soldered directly into a PCB", which is simply them telling you about the standard testing method. It may matter a lot for a SOT-223 but not as much for a TO-220.

In the datasheet they have a helpful note:


  (1) For more information about traditional and new thermal metrics, see the Semiconductor and IC Package Thermal Metrics application report, SPRA953.


I suggest you read it, since you are so interested in the details. I just skimmed through it and it looks interesting. Presumably it will detail exactly what they mean with the numbers, and why the look "better" than the other components.

Conclusion

I don't think they lie - trust that value but apply the usual common sense derating. Assume that the figure is for an ideal test case scenario.

I have a hunch that the other values you see may be too high. Reputable manufacturers don't want to publish lies, so if something is hard to measure they will publish the higher number.