There are differing interpretations of this. Yours is one, and I've wrestled with this one for awhile now.
Did Jesus claim to be God, did he claim to be the Son of God, or was the Son of Man? Let's examine this.
When John the Baptist baptized Jesus in the River Jordan, he heard God's voice saying "This is my Son with whom I am well pleased."
Likewise, when Jesus was put on trial it was because he claimed to be the Son of God.
The Bible tells us (pardon me, I don't remember the exact scripture for this) that Jesus is God in the form of Man.
Elsewhere in the Bible (and there are several references for this) Jesus says he is the Son of Man. Now, who would the Son of Man (as in all Mankind) be, other than the Son of God?
As Jesus was on the Cross dying for our sins, he cried out "Father, why have you betrayed me?"
Now, I'm no Biblical scholar. I can't quote scripture chapter and verse as some around here can, but I think the Biblical evidence here is pretty clear.
As always, I do reserve the right to be wrong, and in doing so recognize that I might be getting an education in the process. :)
Regards,