at schoolを置く場所は？

以下の文での"at school"がおいてある場所についてですが、
"her friends" と "at that time"の間に"at school"をおいてはいけないのでしょうか？
どなたか教えていただけませんか？

She couldn't have met her father at noon today.
I saw her at school eating lunch with her friends at that time.
↓以下のように書き換える
She couldn't have met her father at noon today.
I saw her eating lunch with her friends at school at that time.