It appears that the complaint wasn't so much that the person was on the phone, but that being on the phone in an open area was interfering with someone else's ability to get his or her work done. Having worked with someone who was frequently on personal calls that were so loud that I could not hear business calls that were critical, I can tell you how annoying this can be. It is not discrimination or harrassment to complain that others are interfering with your work. If it is not true, then it still may be a perceptual problem. If the calls were short but there were several of them over a two hour period, from the perspective of the person trying to work, it is essentially a two hour call.
Clearly, there is a problem here. Even if the orginal accusation is not true, someone is annoyed enough with your friend to offically complain and his actions will be more closely monitored. Your friend needs to stop making personal calls at work entirely unless away from the work space. And even there, he should probably try not to make more than one or two personal calls a day. Since there was a complaint, his time on the phone will likely be monitored (even though the boss said that he felt the complaint was in error, most bosses will not want a repeat of the complaint and so will be watching to see if there is a problem.) and he will need to make sure that people see that he is not slacking off by spending too much time on personal business. Frankly, unless there is an emergency, it is generally a bad idea to spend any more than 10 minutes per day on personal calls. And most days you should not need to make any personal calls at all.
Once you have been accused of something (even unfairly), it is up to you to correct the misperception through your actions. Maybe your friend doesn't think he makes more or longer calls than other people. That is irrelevant however; he needs to be aware that people will from now on always be paying attention to his calls and to make them short and sweet and not in the open space. He may also need to be aware that the volume of the call may be the real problem. Many people talk louder than they think they do.
Addtionally open spece is a horrible environment for people who need to do concentrated work, so he needs to be aware that his actions really can be disturbing to other people and he needs to keep things relatively quiet while in the open space. If he has had one accusation, the possibility exists that there will be more if the perceived behavior doesn't change. If someone other than the orginal complainer also has a complaint, then your friend's explanation will be less likely to be believed.
Another issue is that accuser didn't feel he could come directly to the person making the phone calls. Generally most people will ask you to go somewhere else if the call is interfering with their work and only go to a manager if the person does not get off the phone. That the person didn't come directly to him can indicate that your friend already have a poor working relationship with at least one of his colleagues. Your friends needs to see about building better relationships with the people he shares space with. At the very least he needs the good will of the others in case this person has decided he doesn't like your friend and is trying to make life miserable for him with offical complaints. He will want people to stick up for him and say that what is being complained about isn't true or management will get the feeling of where there is smoke there must be fire after several complaints.
It is always critical to build good working relationships with those you work with and those people you sit near. Someone who is getting workplace complaints can't afford to be unfriendly to co-workers or unhelpful to them or try to pretend they don't exist. I know some people would prefer not to interact with their collaegues but this is a mistake of massive proportions in the workplace and all to often results in people who dislike you taking steps to make sure you are gotten rid of. It is never enough to do your job well, you have to manage the perceptions of your bosses and co-workers as well.