It is an expression that means he believed him. The teacher did not believe or trust whatever Tom was saying (the teacher doubted it), however Tom's explanation may be true so the teacher assumed that what Tom said was true.
For example:
"Although he found it hard to believe Tom's explanation, the teacher decided to believe his explanation even though he doubted the explanation."
That is a hard expression to explain, and I don't think I explained it very well, hopefully someone else can add more.