Did Peter's vision of a sheet with animals portend the acceptance of non-Jewish Christians?

According to the story in Acts 10, Peter had a vision of a sheet full of animals being lowered from heaven. A voice from heaven told Peter to kill and eat, but since the sheet contained unclean animals, Peter declined. The command was repeated twice, along with the voice saying, "What God hath cleansed, that call not thou common" and then the sheet was taken back to heaven.

At this point in the narrative, messengers sent from Cornelius arrive and urge Peter to go with them. He does so, and mentions the vision as he speaks to Cornelius, saying "God hath shown me that I should not call any man common or unclean" (Acts 10:28). Peter related the vision again in Acts 11:4-9.

Biblical scholar Simon J. Kistemaker suggests that the lesson God taught Peter in this vision is that "God has removed the barriers he once erected to separate his people from the surrounding nations. He argues that hthe vision means Peter has to accept Gentile believers as full members of the Christian Church, but also that God has made all animals clean, so that "Peter with his fellow Jewish Christians can disregard the food laws that have been observed since the days of Moses.

Others suggest that the implication is that all things God created are declared clean by him, and are not affected by human discriminations.

Frankly, all this interpretation seems to me to be a bit of a stretch - however well intended. Does this passage really overturn all the elaborate dietary laws we have been reading through late Exodus into Acts? And how did Peter make the leap from God's cleansing of the animals offered him to the concept that all men are acceptable by God into the Christian faith?