Interestingly, this does work:

use strict;

my $temp_value = q(\'/Path/to/log.txt');
print "1> $temp_value\n";

my $value = eval $temp_value;
print "2> $value\n";
print "3> $$value\n";

my $foo = $$value;
print "4> $foo\n";

$value = $foo;
print "5> $value\n";
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So assigning to an intermediate scalar works. That seems to indicate a problem in the assignment statement. But that looks legal to me ...