Gotta read the paper closely...
Regarding the bit about SLC being no more reliable than MLC, they also said "within typical drive lifetimes" - an SLC drive has more endurance and a higher expected lifetime under a high write workload, and so the statement isn't really that surprising. It's really just saying that regardless of NAND type, SSDs are lasting as long as they are supposed to.
And yes - the NAND chips used for SLC/MLC/TLC are the same, every cell stores a single analog value. The differences are in how the controller evaluates that analog value, and whether it can differentiate between 2 values (SLC), 4 values (2-bit MLC), or 8 values (TLC). Taking the same analog range and splitting it more ways makes things harder, which is why MLC/TLC is slower and has lower endurance. Well - thats probably not the most technically correct way to put it, but is generally true - go google it yourself if you want really technical descriptions.
As to the way they grouped up the different kinds of drives - keep this statement from the paper in mind:
"The drives in our study are custom designed high performance solid state drives, which are based on commodity flash chips, but use a custom PCIe interface, firmware and driver." So the only thing these have in common with the drives we see are the NAND chips. They do have the details on the process used for the NAND, but the manufacturer data has been cleansed down to 'vendor 1', 'vendor 2', etc.