Just for the record, I live smack in the middle of the tornado area and there are many, many, many rental units that do not have basements. I do not know of a single landlord that gives a tenant the right to shelter in a property they don't live in unless it is a common area, let alone the basement of the landlord's own home. In my opinion those who are chastising the OP for not wanting to allow that are being 100% unreasonable (sorry guys but that is the way that I feel).
If you do not have a basement the next place to shelter is in an interior room with no windows (usually a bathroom). I don't have a basement in my own home and that is what we do.