Whoever keeps the log owns the AI
Companies worry about being locked in to an AI provider through its model or its interface. Those can be changed: models are swapped, interfaces are wrapped. The lock-in that matters sits one level deeper, in the log, the complete history of what your agents received, what they produced, which tools they called and what came back.
The log is the agent
An agent that has worked in your company for a year is not the model it runs on. It is that year of history: the requests, the corrections, the results, the context it built up. The model only interprets that history. Give the same history to another model and the work continues. Lose the history and you start again from zero, even with the same model.
A summary or a transcript is not enough. The value is in the full sequence: what was tried, what failed, what a person corrected and why. That is what lets you check past behaviour, find the cause of an error, and resume work after an interruption.
Where your log lives today
If the log sits only on a provider's servers, kept under their retention rules and readable only through their tools, then the provider owns your agents in practice. You can change the model you point at, but you cannot take the history with you. The day you want to leave, or the day the provider changes its terms, you discover what you did not own.
Four questions to ask
Where is the full log of our agents stored, and in which country?
Can we export it completely, in a format we can read without the provider's tools?
Can we replay it: take a past case and rerun it to check what the agent did and why?
How long is it kept, who decides, and can the provider delete it or use it without our agreement?
If any answer is unclear, put it in the contract before the agents do important work, not after.
The practical rule
Treat agent logs like your accounting records: they belong to the company, they are stored where you control them, and they are kept for as long as you decide. You already own your orchestration and your data. Own the log too.