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Both are right.
Your buddy is right that you can't use a single phase AC motor and dc vfd controller.
Bruno's right that a fixed or variable speed AC motor is basically the same. Usually, only...

Your first link doesn't work.
Need to know the voltage rating of the treadmill motor to be able to answer.
If it's a dc motor, @ either 90 or 180 volts DC it will. The leeson output goes to the...

I won't say how much I spent on my vfd and leeson combo for my belt sander, but those prices are about right.
Used 90 vdc motors in the 1750 RPM range can go for under a couple hun and usually just...

I have a similar lesson drive controlling a variable speed sander I built.
The input plugs into your wall @ 110 vac.
The output will drive either a 90, or 180 vdc motor. You can wire the output...