One of the reasons I find this unpersuasive is that even if Paul did not feel the need to quote Jesus, he would have needed to deal with opponents who did. In Galatians, Paul describes his disagreement debate with Peter and James over whether pagan converts needed to be circumcised and observe the Jewish laws. Surely, Paul's opponents would have cited Jesus own words in support of their position:
Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. Anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.Matthew 5:17-20. If Jesus' words were known and considered authoritative during Paul's time, it is difficult to see how he could address these issues without touching upon what Jesus had to say on the subject.
I can accept that Paul thought that Jesus was an actual person who had walked the earth, but it is hard for me to see how he could have thought that anyone he knew had personally interacted with Jesus while he had.