Its not clear to me what the "avoiding dereferencing side effects" part of the documentation means exactly, however I feel pretty confident in saying that it isnt relevent here. When you do

$hash{key}.=$str;
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there is no dereferencing going on. With

$hash->{key}.=$str;
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there is, however it happens before the .= operator is involved, so it doesnt explain the special casing behaviour of .= and other mutator operators. It turns out that the documentation of this behaviour is not to be found in perlop, but rather in perlsyn (in the section Declarations):

Operators such as ++, --, +=, -=, and .=, that operate on undefined le
+ft values such as:

    my $a;
    $a++;

are also always exempt from such warnings.
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Hope this clears things up for you.