First, though, I want to say I agree with you that seeing the context can indeed help in aiding our understanding. That is where I get hung up here, since Jesus called out the Scribes and Pharisees as hypocrites (all throughout Matthew 23, but also elsewhere). If, as you are suggesting, the Scribes and Pharisees taught only what everybody already knew (the Law of Moses as already established, presumably in writing, although I don't think literacy was a requirement for being under the Law, was it?), why did Jesus urge his disciples specifically to follow these hypocrites' teaching (it's right there, at the beginning of the chapter in which they are called hypocrites time after time, so it's not like we're talking unrelated parts of Scripture) rather than just telling the disciples to follow the Law of Moses?
He was speaking to the crowd and his diciples...so here we have Him telling them to pay attention to what the law says....in other words pay attention to what the scriptures say...what is written..what they knew or if they didn’t to pay attention.....and also that as he listed off the woes etc. he clearly was telling them their teachers were frauds....
People were listening to the false doctrines taught by the Pharasees and these were not convicting people rather they were a chain around their neck.....as is done still today we are taught to pay attention to the scriptures, what Christ says....
You cannot follow fraudulant teaching which is not supported by the scriptures......the only way one can not be deceived and led astray is to know what the scriptures say....Jeusus pointed them to the Law of Moses which was the ten commandments...he then points out the frauds the Pharasees were.