That is not entirely true. If you buy four separate DIMMs you run the risk of getting DIMMs from different production batches. "Kits" are matched from the factory based on the individual operating characteristics of the DIMMs, meaning all DIMMs are guaranteed to work together at the rated frequency and timings. You don't have that guarantee if you buy the DIMMs separately, although there is minimal practical difference.
Correct. Ideally you want to buy a pair in a kit. But the logic could seem to extend to different kits of the same speed and model, although it would be obviously much more important to consider how each module in a kit is matched to its dual-channel partner.
Proof of the pudding, though, should be found in the SPD summaries revealed by CPU-Z or similar utilities like AIDA-64. I bought a kit of 2x4GB G.SKILL "GBRL" 1600 modules in mid-2011; I bought a second kit of the same a year or so later. While the voltage, speed and latency specs are identical, the SPD data is slightly but noticeably different. But as XMP and otherwise stock settings, the two kits overlap.
And -- I was able to fill four slots with them and OC them to a very stable DDR3-1866 at the stock spec voltage and common looser timings.
For some RAM makers (I can only speak from particular first-hand experiences), one might pick one kit spec'd at a higher speed (one particular model), and another kit spec'd at a lower speed (and different model), and set them at a spec reflected in the SPD of both -- speed, voltage and timings. I say "might."
This latter possibility should only arise when you want to populate all slots and you have a likely candidate kit already handy -- wishing not to buy a "match" to the first kit. And you'd have to accept the possibility that the result could be less than ideal.