I had not tried pulling the LIDAR, but yes, especially where the deadfall is 3-8 feet thick in the logged areas, I can already see spots where their generated topo doesn’t match my work.
For that sort of terrain it's common for classification algorithms to put vegetation (e.g. deadfall, small bushes) into the "ground" class, so when the terrain model gets triangulated using all the "ground" points there is erroneous bumps. If this is the case, you could reprocess the point cloud yourself and tweak the settings being used or make manual adjustments.
I'm not sure of the quality of the linked dataset, so maybe it would be difficult to find improvements. But you knowledge of on-the-ground conditions (and smallish scale of the area) means it's definitely possible.
Also, just in case you haven't stumbled across it, a "Digital Surface Model" (DSM) is different than a "Digital Terrain Model" (DTM)!
(surveying student here, very much enjoyed the writeup!)