In syntax-directed definition, terminals are assumed to have synthesized attributes only, definition doesn't provide any semantic rules for terminals?
It's not a claim; it's a definition. In mathematics, we can define things however we want.  [See Note 1]
Our only obligation is to make sure we've shared the definition with our readers.
In any event, it doesn't make the slightest difference. If we want to define an inherited attribute for a terminal, we can just replace the terminal throughout the grammar with a non-terminal with a single production whose right-hand side consists only of the terminal. Then the surrogate non-terminal can carry whatever attributes we want it to carry.
This transformation does not in any way affect the parse (provided it is done consistently throughout the grammar).

Notes

It's not a coincidence that Lewis Carroll was a mathematics professor.