how can it do this when the block is rejected? Doesn't the block need to be accepted to fix the difficulty problem first?
As said, that's my non coder thought: As long as none of the new blocks gets accepted so doesn't any change within it, not?
Nope. Difficulty is calculated by the miner before calclutating block hash as the part of the block template. (function Blockchain::create_block_template() in blockchain.cpp)
If patch decide that difficulty for the next block must be lower miner will spend less time building next block.