Is it possible for the network to reject a mined block if it doesn't include a high enough sum of transaction fees?
In other words - if a miner accepts too-low of a fee is it possible for the rest of the network to reject that miner's solution?
No. That is why this is all a much ado about nothing.
If people want to create sub dust transactions, then they can find people willing to relay and mine them. Problem solved. The dust threshold is merely a default. It doesn't invalidate any blocks.
The reality (and the need for the gnashing of teeth and FUD about the death of Bitcoin) is some people simply WANT to spam the network with transactions which will NEVER be redeemed. They also want to do it for free and have the cost of keeping those transactions in the UXTO forever paid by someone else.