Is "ambiguate" a word, or is there a word with a similar meaning?

A good word for this is obfuscate:

he obfuscated the details.

It implies intentionality, as well as hiding "in plain sight".

From vocabulary.com:

Some people are experts at obfuscating the truth by being evasive, unclear, or obscure in the telling of the facts. The people who are good at obfuscating would include defense lawyers and teenagers asked about their plans for Saturday night.

Although the verb obfuscate can be used in any case where something is darkened, less clear, or more obscure, it is most frequently used in reference to things like ideas, facts, issues, or the truth. The usual implied meaning is that this obfuscation is done deliberately. Politicians often obfuscate the truth about the issues to win support for their positions so they can win elections.