It is much more complicated to follow up on an anonymous tip than it is if you have someone you can contact and get the details from. On top of that if a company fails to act on an accusation of fraud, or illegal activities, they can be held criminally and civilly liable.
So lets take this example "anonymous" tip:
Bill Jones in billing is double billing some of our customers.
So as the compliance department we decide to act on that tip and investigate. However because he is good at hiding it and we do not have specific details we are unable to find any evidence to support the accusation.
A year or more down the road a customer figures out what happens and it becomes a big deal. In an attempt to save your job and avoid possible accessory charges you point out that you informed the compliance team. Now the compliance team is implicated because you informed, but they did investigate but found nothing to substantiate the claim.
Now if that tip were not anonymous the team could contact you and find out what exactly you think is going on, and follow up. And some actions may require a witness, this is especially true if you are witness to harassment or discrimination. Many times it is impossible to make a case with out someone to act as a witness to the activities in question.
There is also a culture of personal responsibility and accountability they may be trying to encourage. This type of culture is especially important in companies where there is a potential for abuse of trust or power. If you feel strongly enough to report the activity then you should be willing to do so with out hiding behind the cover of anonymity. While this culture does not make sense in all environments or industries, there are those where it may.
By not allowing for anonymous whistle-blowing, the company is also forcing itself into a higher expectation with regards to whistle-blower protection. Failures on the company's part in this regard will most likely be more heavily punished by regulators, or in civil court.