Jelly, 9 bytes
S;§>Ƈ1S=L
Uses Unrelated string's test suite.
Explanation
S;§>Ƈ1S=L
S sums of columns
; concat with
§ sums of rows
Ƈ keep the sums which are:
> 1 greater than 1
S sum of that
=L = input length?