Chemistry - Comparison of basic strength of benzylamine and ammonia

Everything you said is correct, except that it is more relevant to consider the inductive effect of methyl on nitrogen: electron density is donated to nitrogen.

The inductive effect of phenyl is on the methyl, decreasing its ability to donate electron density to nitrogen, but apparently not completely.

I suppose that if you increased the negative inductive effect of the phenyl group with a couple of nitro groups, the basicity of the compound would decrease.