One of my former coworkers (whom I'll call Doug) had his boss at a previous job more or less do this on his behalf. Doug had been working for a small company that was acquired. The new owner asked the boss of the smaller company what Doug had been making. The old boss reported a number much higher than Doug's actual salary. The new ownership just said "sounds reasonable" and Doug immediately got a massive raise. Doug said he was a little uncomfortable that a lie had been involved, but he didn't feel he could contradict his boss, so he went with it.
I'm not exactly sure why the circumstances didn't involve the new employer from actually checking his previous salary, but based on my interaction with Doug I'm sure the story is true.
This is the boss saying “Doug was worth more than I could pay him, here’s what he should be getting” which is actually a very nice thing to do for the new ownership because losing Doug soon after could have been devastating. Likely the small company had felt it couldn’t match the actual salary (and likely tried to make it up in other ways).
I'm not exactly sure why the circumstances didn't involve the new employer from actually checking his previous salary, but based on my interaction with Doug I'm sure the story is true.