I have nearly been to Beijing. = I got the ticket, arrived at the station, but then I got a call and had to cancel my planes. So I nearly went there, but not quite. I think the other one is self explanatory.

They are right, depending on your meaning, but one is nonsensical. If we say "he has nearly been to every country", it implies he drew near to the country, but did not actually set foot. If we say "he has been to nearly every country", then it means he has traveled to almost all countries.

"He has been to nearly every country" would mean he has been to almost all the countries in the world. "he has nearly been to every country" Sounds more like he missed his flight to go the countries. Like he almost went but didn't. In the second sentence you're saying you nearly did something. Which means you almost did something. For example if I said: I nearly made out the door on time. That would mean I almost made it out the door on time, but didn't. Or: He nearly won the race. Would mean he almost won, but didn't