Ehrman is a fascinating scholar, swinging radically between perspectives throughout his career. He's obviously quite intelligent and it also seems like he wholeheartedly throws his entire being into his research, which is why you can account for such radical opinions. They become a part of his very being.
The primary medium by which information was communicated was through oral transmission. Even once the written medium became relevant, oral transmission was the primary means of replicating information. There are a few issues to take up with Ehrman's perspective.
First, he is being intellectually dishonest in his presentation of oral tradition. I am pretty sure that he has a better understanding of orality than he's letting on, but that would sell fewer books. The reality is that though the primary way of transmitting important information, the written word was still present far back into antiquity. For instance, the Ketef Hinnom Amulet, which dates to 600 BCE, has an inscription of the Aaronic Blessing (Numbers 6:24-26) which played a role in the temple cult of ancient Israel.
Because of the centrality of oral transmission in the role of life, and worship, this was not just an isolated "game of telephone" that followed one line. There were many, many, many parallel streams of transmission that coursed through each family, tribe, and the nation. One must imagine that, given the centrality of the edicts to the way of life of Israel, that an out-of-sync stream would be corrected. Though Israel did not always follow the mandates of the temple cult (the order of worship), the laws were intricately intertwined with the daily life of the people. There was no such thing as the separation of church and state (which is a fairly new concept).
Secondly, Ehrman's claim that this was like a grand game of telephone is a classical case of an anachronistic fallacy. It would be like questioning the validity of The Lord of the Rings because J.R.R. Tolkien used the antiquated medium of writing in whole words and complete sentences, whereas the present form of communication would be in SMS shorthand. ZOMG Blbo, U gave da ring 2 Frodo?? The inability of the present generation to accomplish a task does not disqualify previous generation from such a feat - especially when there is a tremendous amount of technology that no longer necessitates such direct recall.