:)) Мне тоже натуральнее звучит to speak to, но честно говоря не озадачивался...пока))

I like this explanation:

According to The Columbia Guide to Standard American English,

"In most uses these combinations are interchangeable: I spoke to [with] her for only a few minutes. In some instances, however, there may be semantic distinctions: Speak to sounds a bit more one-sided, perhaps, than speak with, which may imply more give and take. And in one sense speak to suggests strongly that the speech is to be both one-sided and admonitory: I guess I must speak to him [about his behavior]. Talk works much the same way, except that you speak to [on the subject of] an issue far more often than you talk to an issue."

Mutually! You are lucky to have experts around:)