I don't know your source, but the term "diatonic scale" typically refers to the major scale and its rotations (i.e., the modes). As such, we can test this claim just by looking at the intervals of a major scale.
- All seconds within in the scale are either minor (E–F and B–C) or major (C–D, D–E, F–G, G–A, A–B).
- All thirds are either minor (D–F, E–G, A–C, B–D) or major (C–E, F–A, G–B).
- All fourths are either perfect (C–F, D–G, E–A, G–C, A–D, B–E), or augmented (F–B). There's one augmented interval!
And conveniently, we don't have to do the rest of the work. Due to intervallic inversion, we know that seconds invert to sevenths, thirds to sixths, and fourths to fifths. Furthermore, we know that the qualities invert in particular ways, and only diminished/augmented intervals invert to each other.
As such, the only diminished/augmented intervals of a fifth, sixth, or seventh is the diminished fifth.
So yes, in fact, your source is correct: the only augmented/diminished interval that appears in the diatonic scale is the tritone.
You may be thinking of the augmented second (and its inversion, the diminished seventh) that is included in the harmonic minor scale. But this scale is not usually considered a "diatonic scale" since it requires a chromatic pitch: the raised leading tone.
Or, you may be thinking of enharmonically spelled intervals. C to E is a diminished fourth if E is spelled as F♭. But if you're suddenly using F♭, you're no longer using just the notes of the diatonic scale. Even though F♭ is enharmonic to E, they are distinct pitches, and so using that pitch violates the premise of the original question. It's the same as the augmented seventh between C and B♯. Since B♯ isn't in the diatonic scale, we must think of this interval as C to C, which is a perfect octave.