Not quite correct. In fact, there is no such thing as SAE 10.

Yeah. I raised the same objection a few years back when someone said "there is no 10 weight oil".
It's a 20 weight that can't be called a 20 weight because it has an HTHS below 2.6 (or so I'm told).
So, effectively a 10w is a 10w(unqualified)20.
..but for all practical discussions ..regardless of our evolutions in intermediate this and that ..the basic premise for the 5w- and 10w designations (which occurred "back in the day" of Group 1 oils. A 10w-30 was a 10 weight (equivalent CST) basestock. They chilled it to all the respective temps and called that "10W" ..they then doped it with VII until it met 30 weight viscosity @ 100C.
Now you can achieve 5w-30 with a 10 weight-like CST (100C) basestock due to improvements in VI with Group II and II+ technologies.
..but the standards/assignations never knew of these things when they were created. They were dealing with 90VI Group I oils.
So, as technically incorrect as the notion is in a contemporary sense, the designations are founded on the premise that the multivisc oil appears exactly as it reads at the respective conditions. It appears like a 5 weight at xxxF. It appears like a 30 weight at XXXF.
Any introductions of PPD and whatnot is a further manipulation to enable these appearances.
So ..is a cigar sometimes just a cigar?