I would get a second opinion.
Xrays are always a good idea if there's a suspicion of an underlying issue, like elongated roots. However, generally when xrays would be recommended would be a time when a pig DOES have symptoms of teeth issues but when the vet opens the mouth, all seems well.
Based only on what you're saying here - his behavior, appetite, lack of other symptoms that indicate an underlying tooth issue - I myself would have to doubt whether or not the pig was really having serious teeth issues.
You could have the tooth trimmed and see if the problem goes away or not, especially as long as he's eating normally and his weight is steady.
Or, you could always agree to do the xray, get the results and go from there. There's no reason that they'd do an xray and move immediately to a tooth extraction, except to save him from undergoing anesthesia an additional time, but in this case I'm not sure that's worth much.
However, at his age, I would be quite reluctant to race into anything that might not be necessary to begin with.