I am not well versed with the way perl parser works. But I took the help of Deparse backend and this is what it revealed.

>> perl -MO=Deparse -e 'do ("print")'
do 'print';
-e syntax OK

>> perl -MO=Deparse -e 'do (print)'
do print($_);
-e syntax OK

>> perl -MO=Deparse -e 'do print'
do 'print';
-e syntax OK

>> perl -MO=Deparse -e 'do{print}'
print $_;;
-e syntax OK
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do expects a BLOCK, SUBROUTINE (deprecated) or an EXPR as its argument. So, I am guessing that, when a BLOCK or SUBROUTINE is not passed, it is looking for an expression and probably allowing barewords.