Why does unicode-math break the kerning of accents in combination with amssymb?

Question

I am using the following MWE. First time with unicode-math, second time without it:

% arara: lualatex

\documentclass{article}
\usepackage{amssymb}
%\usepackage{unicode-math}

\begin{document}
$\tilde\Box \hat\Box \bar\Box$   
\end{document}

Where does the difference come from? The kerning is clearly broken.

amssymb.sty 2013/01/14 v3.01 AMS font symbols

unicode-math.sty 2013/05/21 v0.7e Unicode mathematics support for XeTeX and LuaTeX

Edit

Barbara Beeton suggested to try the package latexsym instead of amssymb. This results in worse vertical positioning and the very same effect for I/O unicode-math:

% arara: lualatex

\documentclass{article}
\usepackage{latexsym}
%\usepackage{unicode-math}

\begin{document}
$\tilde\Box \hat\Box \bar\Box$   
\end{document}

Answer 1

You shouldn't be using amssymb together with unicode-math. The \Box command can be substituted with the (not really clearly named) \mdlgwhtsquare command (for U+25A1 WHITE SQUARE).

% arara: lualatex

\documentclass{article}

\usepackage{unicode-math}

\renewcommand{\Box}{\mdlgwhtsquare}

\begin{document}
$\tilde{\Box} \hat{\Box} \bar{\Box}$
\end{document}