Because Jesus is divine, and our redeemer, of course he accepts those who come only to Him.
Matthew 15: 21-28.
Anyone familiar with their Bible would immediately remember the Canaanite woman who cried out to the Lord that He might have mercy on her demon-possessed daughter. He was surrounded by the crowd, His own, as she called out to him. He said to her, “I was sent only to Lost Sheep of the House of Israel.”
(Theologically, this is said because Christ had not been crucified and the Holy Spirit not given. It was after Christ’s ascension that the disciples were told that salvation was for the Gentiles as well as the Jews.)
“Yes, Lord, but even the dogs eat from the crumbs from the table of the children”, when she cried out to Him through the crowd, “Have mercy on me”. “Woman, your faith is great,” said the Lord, and He healed her daughter.
In other words, here we have a situation that is exactly as you described. People forcing themselves upon Jesus alone, ignoring those who were “His own”. And he accepted those people.
Is this intended to teach that it is necessary to come to Jesus through Mary? If so, that is certain heresy. We may accept and love our Mother, but no saint in the Church is intrinsic to salvation, even the Blessed Mother.