This paper analyzes the design and competitiveness of four neural network (NN) architectures recently proposed as decoders for forward error correction (FEC) codes. We first consider the so-called single-label neural network (SLNN) and the multi-label neural network (MLNN) decoders which have been reported to achieve near maximum likelihood (ML) performance. Here, we show analytically that SLNN and MLNN decoders can always achieve ML performance, regardless of the code dimensions -- although at the cost of computational complexity -- and no training is in fact required. We then turn our attention to two transformer-based decoders: the error correction code transformer (ECCT) and the cross-attention message passing transformer (CrossMPT). We compare their performance against traditional decoders, and show that ordered statistics decoding outperforms these transformer-based decoders. The results in this paper cast serious doubts on the application of NN-based FEC decoders in the short and medium block length regime.