Too many bad things happen in a case like this. I believe for the development of both children this is a critical moment. Because these are children we are training, teaching, and molding, making peace is not the number one goal as it may be with co-workers, spouses, roommates, etc. The number one goal is the growth of the children.
Issue with the Bully
First, child 1 thinks he can manipulate adults and in a way 'punish' another kid by creating a story. This will increase his desire to manipulate others in general as it is a sense of power and success. Obviously this trend is self-feeding and non-sustainable. Which means this bad behavior will grow worse with time, and eventually fail.
The greatest issue of when it fails is, how will the kid handle this trick of deception not working anymore? In most cases it will bring about anger and not getting the desired effect and being caught in the lie. Anger brings about even more issues. It is critical this be caught early.
There is a long chain of events being started in this moment which leads to a corrupt spirit - if you will.
Just as some people say the threat of global warming is so severe that
we must take action now, so is the threat of the future corruption of
spirit so great that action should be taken now.
Issue with the Victim
Second, the kid who has been lied about also is at risk. First, he will become a victim quickly as the threat of being told on will bring about compliance. If a pattern of bullying develops and is sustained not only will the shy kid give in, he will also learn that the teacher will not protect him.
When more serious problems occur he may not have the trust to bring them to the attention of those whose job it is to protect him. This extends to his parents if they stand idly (hopefully they are at least 'getting his back' at home when they talk about the situation).
As with the bully, the long term threat for the victim is a spiritual
problem of a crushed spirit and the loss of hope in being safe and
Chances are that the teacher (just like we parents) don't want to deal with the issue and probably doesn't have the time for it. 7 year old's are expected to do a lot in school (in the USA) and are already being tested. Issues like this seem small and truly the educational system in the US does not prepare teachers for this type of situation.
Everyone should work together on this situation and while it is possible that the other parent will be defensive, an attempt at the truth should be made. The parent of child 1 deserves to have a chance to know about the behavior or at the very least know to start being a little more attentive to what the child is doing and saying.
A 15 minute parent conference where there isn't any blaming but rather an understanding of what each kid believes happened would be helpful. Probably something without the kids there, where the teacher simply explains the two sides of the story with the only goal of letting everyone be on the same page and know what to look out for in the future. (i.e. where there is smoke...)