There's another problematic spot too, let's say my agent is using the site card I need to recover, now what?
Use equivalent.
Brutal mode is OK too, because it penalize player that is unable to provide site required by HIM (in contrast to WH rules that put responsibility for providing site required by player on its opponent).
There is also one possibility to consider:
what if site required by No Better Use, Sack Over The Head, Use Your Legs is occupied by other company of the same player? If it is not a haven, or not in organisation phase, two companies of the same player cannot occupy it.
Let character join other company (if it does not violate composition rules), or discard character (because card text requires forming separate company, that is not possible).