I think the problem is the initial understanding of what the soil and seeds are.
Mark 4:14 (NIV)
The farmer sows the word
This verse implies that the seeds are the gospel. However, if we look at the next sentence, there appears to be a contradiction:
Mark 4:15a (NIV)
Some people are like seed along the path, where the word is sown.
However, that contradiction is clarified in the next sentence:
Mark 4:15b (NIV)
As soon as they hear it, Satan comes and takes away the word that was sown in them.
Clearly, Satan can't come and take away the people; he's taking away the word that was sown.
Because of this, it appears clear that the gospel are the seeds. This makes it seem clear that the soil is the people.
However, can we really accept the soil as people?
Mark 4:16-17 (NIV)
Others, like seed sown on rocky places, hear the word and at once receive it with joy. But since they have no root, they last only a short time. When trouble or persecution comes because of the word, they quickly fall away.
This is showing that the people are like the seeds that are attempting to grow roots.
I don't think that "the soil" can be equated to people any more than the seed can be directly equated to the gospel (due to verses 16-17). This is an analogy and Jesus isn't trying to make a perfect analogy here, but simply trying to illustrate a point.
If the soil could be equated with anything, however, I believe that it would be equated with the heart, not with the person who owns it.
Proverbs 12:25a (NIV)
Anxiety weighs down the heart
Luke 12:34 (NIV)
Be careful, or your hearts will be weighed down with ... the anxieties of life
So, the question is: Is the third type of soil a true believer? My answer: No.
Galations 5:22 (NIV)
But the fruit of the Spirit is ... peace ...
True believers have the Holy Spirit living within them. One of the results of having the Holy Spirit is peace--not anxiety.
We can also see this here:
Philippians 4:7 (NIV)
And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus.
These verses show a very direct contrast to the "third soil":
Mark 4:18-19 (NIV)
Still others, like seed sown among thorns, hear the word; but the worries of this life, the deceitfulness of wealth and the desires for other things come in and choke the word, making it unfruitful.
This third type of people that we see in the parable of the sower are people who are so burdened with the cares of this world, that they don't nourish their spirit. These people allow the world and the cares of this world to choke out their faith.
They are not true believers.
One last item that you might find interesting.
Matthew 7:2 (NIV)
Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven.
What is the will of God when it comes to worrying?
Matthew 6:33 (NIV)
But seek first his kingdom and his righteousness, and all these things will be given to you as well.