USB port controller, divider mode and BC compliancy
No, they are not. There exist charge port controller chips including TPS2513 (not 2543) or MAX14667 or Cypress chips (see next link) that support the Samsung 1.2/1.2V scheme. Actually, you were unlucky in looking at pretty much the only TI charging chip that doesn't do 1.2/1.2:

 

Also note that according to Cypress app note AN92554 (p. 5), that 1.2/1.2V scheme is only used on Samsung tablets, but the S3/S4 Samsung phones use BC 1.2.

The obddiag page you link to doesn't actually say that the S4 phone uses that 1.2/1.2 V scheme, but only that a "Samsung Galaxy pad device" does. Then it says in Engrish: "The latest Samsung Galaxy S4 and Galaxy Tab charger ETA-U90JWS is using slightly divider values with R1=300K and R2 =100K and the same ratio (0.25)." That info appears rather unreliable because the adapter with that number is intended only for Galaxy Note 2 according to its Amazon page... which I would not regard as terribly reliable either because it's sold by an obscure shop (via Amazon, rather than by Amazon) and some of the comments say the product is counterfeit. There's no page on Samsung's website for that precise part. There is one for ETA-U90JWEBXAR but that is identified only as a Galaxy S3/S4 2A charger basically (plus a few more obscure phones, but no tablets). For their tablets Samsung's website list an ETA-U90JBEGXAR as a 2A charger, but it has no phones (nothing below a 7" screen) listed as compatible. So I think the Cypress app note info is still valid.

Also, I can't find the putative 2.5V/2.5V Samsung info in http://forum.xda-developers.com/showthread.php?t=2274321 Please provide a quote.

The moral of this story is that when it comes to proprietary signaling schemes, you need to read the datasheets very carefully... and shop around. Never mind trusting various Engrish pages on the interwebz.

Finally, regarding port controller auto-detection algorithms... they generally keep their sauce secret. But in the case of the TI controllers, they were kindly enough to shed some light in the case of the 1.2V/1.2V to BC 1.2 mode transition. From their Power Management Guide 2015 (p. 107):


  1.2-V charging scheme is used by some handheld devices
  to enable fast charging at 2.0 A. Certain devices (as shown)
  support this scheme in the DCP-Auto mode before the device
  enters BC1.2 shorted mode. To simulate this charging scheme,
  D+/D– lines are shorted and pulled up to 1.2 V for a fixed duration;
  then the device moves to DCP shorted mode as defined in
  BC1.2 specification.