The amount studios get involved in the details of a story is variable.
However, when a movie does as well as 'The Matrix' the people who are considered essential find they have a lot of power, including the power to say "No." to any input they disagree with.
I'd have taken a chainsaw to those movies and kept the philosphical under-pinning while removing a lot of the explanations; let the characters and actions speak for themselves, but the Wachowski's wanted it all and they got it.
In the years since then they've remained extremely talented, but they could still use some editorial input.