Clarification on evenly dispersing modular hashing
The remark is quite cryptic. If $m = 2^r$, then only $r$ bits of the input affect the value of the hash. But it any other circumstance, all input bits affect the value of the hash.
By the way, your example ($7,17,27,37$ all get mapped to the same value modulo $10$) works for any value of $m$. For example, $7,18,29,50$ all map to the same value modulo the prime $11$.