Enforce \sideset behavior compatible with LaTeX

From amsmath documentation

Note: this command is not designed to be applied to anything other than sum-class symbols.

So,

$ cat example.tex 
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
  \sideset{_*^*}{_*^*}\prod
\end{equation}
\end{document}
$ latexmk -pdf example.tex

works.

But

$ cat bug.tex 
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
  \sideset{_*^*}{_*^*}X
\end{equation}
\end{document}
$ latexmk -pdf bug.tex    
Latexmk: This is Latexmk, John Collins, 5 February 2015, version: 4.43a.
Latexmk: applying rule 'pdflatex'...
Rule 'pdflatex': Rules & subrules not known to be previously run:
   pdflatex
Rule 'pdflatex': The following rules & subrules became out-of-date:
      'pdflatex'
------------
Run number 1 of rule 'pdflatex'
------------
------------
Running 'pdflatex  -recorder  "bug.tex"'
------------
This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(./bug.tex
LaTeX2e <2014/05/01>
Babel <3.9l> and hyphenation patterns for 21 languages loaded.
(/usr/local/texlive/2014/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/local/texlive/2014/texmf-dist/tex/latex/base/size10.clo))
(/usr/local/texlive/2014/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/local/texlive/2014/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/local/texlive/2014/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/local/texlive/2014/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/local/texlive/2014/texmf-dist/tex/latex/amsmath/amsopn.sty)) (./bug.aux)
! Limit controls must follow a math operator.
<argument> X\nolimits 
                      _*^*
l.5   \sideset{_*^*}{_*^*}X

?

Unfortunately, MathJax isn't compatible with this behavior of LaTeX.

This creates problems when users have to create a PDF using LaTeX from a webpage that uses MathJax. Can MathJax be more compatible with LaTeX?

Reproduce the two \sideset examples from the issue in MathJax and compare their behavior with the shown LaTeX output. Trace the \sideset handling and determine how non-sum symbols are treated; done means the behavior matches LaTeX while preserving the working sum-symbol case.