Yup ZD,
You are 100% correct.
And at the point that Rav Chaim Ozer zt”l called all yeshiva bochrim to Vilna it was indeed safer there and thousands were ultimately saved because of their initial trip to Vilna which gave them the time to find escape routes.
This includes the entire Mirrer Yeshiva as well as parts of Kletsk and Yeshivas Chachmei Lublin.