After spending time as both a full time employee (FTE) and consultant, I find the dynamic can quite often be the opposite of what you describe.
To an employee, you are a paycheck / insurance / vacation-time /etc. If they do a great job they will get the same paycheck as if they do a mediocre job. Maybe they will get an extra 1% raise. As long as they don't royally fuck up, they will not get fired. As Peter Gibbons put it, an employee relationship will "only make someone work just hard enough not to get fired."
To a contractor, you are a gold mine. They can make enough in 4-5 months to match what an FTE gets in a year, even counting benefits. And their ability to get more of these gigs in the future is mostly dependent on making each client happy. If they do a great job, instead of a 1% raise they get another 1000 billable hours at $225 each. This is quite the motivation to do a great job.
Both your scenario and my scenario happen. Finding a great employee and a great consultant are both rare and incredibly valuable.