Kawhi definitely deserves max money, just in the same way Tony did when he got his FMVP. Tony turned down max money just the same way Tim and Manu took paycuts.
It's not because Kawhi deserves max money that the Spurs are going to sign him for that much. The Spurs tend to be pretty good at re-signing their players for "decent" contracts, and that usually comes from the fact that the Spurs are good at drafting players with the right character, who value winning and team spirit over $$$.
This is why I wouldn't be surprised to see Kawhi stay in SA for less than the max. Especially after what he said after winning his FMVP, to the tune of "my agent will talk to the Spurs and I'm sure they'll agree on something fair and I'm not worried in the least about it".