Nice to see you are using the platform so actively!
As for your question: I've had a look and found a source by the BMI (Bundesministerium des Innern, für Bau und Heimat), stating that you need
- "mündliche und schriftliche deutsche Sprachkenntnisse auf dem Niveau B 1 des Gemeinsamen europäischen Referenzrahmens für Sprachen"
Translated to English this means:
Oral and writing skills in German on a B1 level, according to the Common European Framework of Reference for Languages.
According to this website, it looks like you would indeed need to have B1 in both sections - writing and speaking.
On the BAMF website about the DTZ, it is stated that...
"To obtain the "Zertifikat Integrationskurs", you must first prove that you have been awarded the overall result of B1 in the "German test for immigrants" (DTZ) language test. This shows that you have achieved an important objective of the integration course."
Here, on the other hand, it seems that an overall test result of B1 is sufficient to apply for citizenship/ naturalization in Germany.
I'm unsure if the responsible authority highly values B1 in speaking and writing, and if that is the reason why the case officer asked him to repeat the test. Maybe it would help to talk to them again and explain that he has an overall B1 test result, which is one of the requirements for naturalization as explained by several websites, and even achieved B2.
Please let us know if you need any further assistance!
All the best,