Your first example doesn't dereference $stat_ref. Your second example dereferences it twice. You have two options:

$first = $stat_ref->[0][0];
    # or
$first = $$stat_ref[0][0];
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I think this is documented in perlreftut. It's a hard concept to grok the first time around. I stumbled over it for a couple of weeks, myself.