I can give an example of one of the scenarios you describe.
I bought my mx5 in January with no service history from a dealer. A 2003 2.5 with 24k on the clock. I took some care buying it. I wanted to use a dealer as even though I may pay a little more they generally come with warranty (even if only 3 months) and you have somewhere to return the car to if you have issues.
I took a friend with me to the dealers and he spent gave the car a thorough check (he dissapeared under the car one point, I just saw his legs poking out!). I then took the car for a drive and checked the common faults. There were no signs of rust and the car looked fine. One sensor needed replacing before I picked the car up which the garage paid for.
I had an MOT history from the dealer and performed a HPI check, all looked good. The car was MOT'd as I bought it and given a basic service (oil etc).
The additional thing I did do is buy the extended warranty so it lasts a full year (it came with 3 months). This has allowed me to drive the car in confidence and also when I checked my car in for it's summer(ish) service this month I was able to ask the Garage to give the car a check and let me know if anything covered on the warranty needed doing. I'll ask for the same on it's MOT the month before the year is up.
To date my car has been wonderful, now up to 28k on the clock and still running like a dream.
I took a gamble and so far it's been good for me but I took my aggressive (bad cop) friend with me to buy the car and I have used all the tools I have to give myself peice of mind. Whatever you decide, good luck and enjoy the drive