Like I said, "run through the shop" can be very subjective depending on the audience. Hindsight of course, you would be much more specific. I am not as against buying something sight unseen as others are on here. Certainly can be a risk. However, if you take some precautions I think it can work out, has for me.
I bought a 590SN from Ziegler Cat in Mn, The machine had 1100 hours on it. I asked for and received their trade eval when they brought it in. I paid Titan equipment (Case dealer) to do the same evaluation that they would do if trading it in and had them send my the docs supporting. Great experience, Cat was professional, the machine was as stated. I bought a 721G from a soybean company somewhere in Iowa. Machine had 1400 hours, I had my local Case dealer confirm the VIN, it was purchased by the company I was buying it from. I paid the local Titan dealer to go over the machine. They also had a service agreement with this customer so I was able to get that info as well. Machine was as it had claimed it to be. Last year I bought a WN ET90 from an independent equipment dealer out of Eastern Washington. I internet checked him to the fullest extent I could. I was more nervous about this, couldn't get a WN dealer to do an inspection on it. I did confirm through WN that it was sold out of Missoula, MT. I asked for and received a boat load of videos and camera shots. Turned out great. Machine was as it was said to be.
I try to always have a machine checked out by a third party when I can. It provides more info than I would get had I flown in somewhere to drive it around the yard and the cost is less than showing up yourself. There are lessons to be learned here for many of us, phrases like "run through the shop" or 'have the machine checked out by service need to be followed by specific instructions and written documentation that supports what they said they did.