Your conclusions are wrong. STDERR is being captured and stored in $x.

$ cat asdf
#!/bin/sh
echo "line 1"
echo "line 2"
echo "line 3" >&2
echo "line 4" >&2

$ perl -le'$x=`./asdf 2>&1`; print "<<Captured $x>>"'
<<Captured line 1
line 2
line 3
line 4
>>
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Using backticks in list context will split the lines if that's what you want.

$ perl -e'print "Captured $_" for `./asdf 2>&1`;'
Captured line 1
Captured line 2
Captured line 3
Captured line 4
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