I know the DEFLATE standard intimately and implemented a decoder and encoder (open source on my website/GitHub).
We know that the smallest image requires 2 bytes - 1 for the row filter and 1 for the pixel(s). For simplicitly, we'll assume the data is (hex) 00 00.
A DEFLATE compressed stream must have at least one block. There are three choices for each block's type - uncompressed, fixed Huffman code, and custom Huffman code. Uncompressed requires 1 byte for {type (2 bits), finality (1 bit), padding (5 bits)} and 4 bytes for the length. So that uses 5 bytes already. Using a fixed Huffman code block lets us encode those 2 bytes as 4 bytes. Using a custom Huffman code requires many, many bytes just to specify the Huffman table. Hence, the OP article's approach is justified.
But by exhaustive search of all DEFLATE blocks that are one to three bytes in length, I can confirm the article is correct. All of them decompress to (at most) one byte of data.
Which isn't a surprising result, but I wasn't actually sure of it before trying it out.