I like how things get twisted and misunderstood. I am pretty sure that nobody from FEMA or Tennessee's department of emergency services ever said "don't give your neighbor a helping hand or a towel/socks/shirt". Instead, what they are intending to prevent is people from ND donating a shovel, towel, blanket, clothing, etc up here in Bismarck, ND that has to then be transported to Tennessee. Emergency management agencies partner with NGOs (Red Cross, Salvation Army, etc) and may recommend donating cash to those NGOs, which can easily be converted to supplies that are specifically needed and mass transported to the area in need of help. And hell, I am not sure I've ever seen an example where FEMA accepts donations in the first place.
As far as FEMA or TEMA as she said wouldn't go into areas with closed roads, again...if my guess is correct and she's misinterpreting an advertisement for the NGOs, that's right. Red Cross and the Salvation Army doesn't show up with a bulldozer in hand to clear a road. That needs to be the local highway dept, National Guard, whoever, but someone with those resources.
The whole intent here is to encourage people from ND to save your donations of physical goods for your local charities, not these large disasters halfway across the country.
Anyway, that would be my guess since I have seen it before.