It is grammatically correct to say “He is at a meeting.” But it is also grammatically correct to say “He is in the meeting.”
So how do we know when to use at and when to use in?
When we are making reference to someone being generally at a location we use the word at. For example “He is at the office” which means that he is somewhere at the office – he could be in his office, at the water cooler, gone for a meeting, we don’t really know, but he left work this morning for the office, so he is at the office.
But you can also say “He is in the office.” “Where is the boss?” “He is in the office.” That means that right now, while we are speaking; he is in the office. He is not outside the office, or somewhere around, but he is in his office, probably sitting at his desk.
The same logic follows for the meeting. “Where is the boss?” “He’s at a meeting right now and will be back later.” Is he sitting in the meeting at this very moment? It is possible, but he could be on his way there, sitting in the meeting, outside the building or on his way back from the meeting. He may not necessarily be sitting inside the meeting room. But if we say, “The PM spoke about the country’s economic state in the meeting”, that means that he spoke during the meeting, in the meeting, at the beginning, in the middle, at the end of the meeting, but he spoke in the meeting – while it was going on.
I hope this explanation has made the usage of in and at a little easier to understand.