Is it possible for a bicyclo compound to have three bridges of equal length?
Why not? The simplest bicyclic bridged compound, bicyclo[1.1.1]pentane, is a well-known example of such a molecule for its use in synthesizing the even more strained propellane. I believe your teacher was trying to prescribe the rules of bicyclic nomenclature, i.e.


  In between the prefix and the suffix, a pair of brackets with numerals denotes the number of carbon atoms between each of the bridgehead atoms. These numbers are arranged in descending order and are separated by periods.