The IANA registry mentioned in the question cites RFC 2978, which in turn cites several RFCs which define how character encodings are to be specified in the Internet. Thus, since ISO8859-1 is not listed there, it is not correct to use it.
Programs may still accept it, as part of their error recovery, but they are not required to do so. Programs may do better error recovery, upon encountering an undefined character encoding name, by inspecting the actual content of text data and trying to make a guess on the encoding. Or they may simply fall back to some default encoding they use, and this may well be ISO-8859-1 (or, in fact, more often windows-1252).