Yes the new tivo responds to the same codeset as the Directv branded receivers. But there will be certain keys that don't, like the power commands, tivos don't have them.

But if your White remote were set to RF mode, or an alternate IR codeset from 00002-00008, the remote won't work.

But just programming in code 00001, will take the remote out of RF mode, and set it to default codeset, will it should control it.