This message only means what it tells, that PHP script is able to create, delete and modify files without special allowance. That's all.
Since miniBB doesn't require to operate on files by default, this operation has some risk in background - if there is a vulnerability found in some of the scripts, hackers could easily put extra scripts on the server, because the server just allows it.
But this is not the common case. miniBB just warns you that it's dangerous. However it will run with no problems, even if such message is reported.
Most likely, this doesn't depend on permissions you can set, it's up to the server's permissions. Most of nowadays providers allow PHP scripts to operate on physical files in client's folder by default. This is mostly done for "auto-update" programs, which could overwrite PHP files without special asking.