Yes, there are implemenations of hash tables that solve this problem. Hash collisions still ruin your worst case performance, but as long as nobody is asking how long you spend on inserts you can solve that too. As a trivial example, on each insert make the hashtable larger and change the hash function randomly until you found a solution that has O(1) lookup for all elements.

But now we're far outside the realm of "properties of hash tables" and instead inside "properties of my hash table", and any decent interviewer should recognize that.