Yes, the context-free idea isn't a logical necessity for expressing in BNF, because that alone can be conquered by expressing the different context types as alternative BNF definitions.

Rather, the most compelling arguments that have been made in reply here come from those perl syntax elements which overpower the nearby context, such as (amongst other examples given by various people) the e-regexp modifier.

non-a-slash:    # string that doesn't contain a non escaped slash
SUBSTITION:     non-eval-substition | eval-substitution
non-eval-substitution:
               's' '/' not-a-slash '/' not-a-slash '/' non-e-modifiers
+(*)
eval-substitution:
               's' '/' not-a-slash '/' slashless-code '/' e-modifiers(
+*)
non-e-modifiers: 'x' | 's' | 'm' | 'g' | 'x' | 'i'
e-modifiers:     'e' | non-e-modifiers
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Grammars expressed in BNF can be parsed with recursive decent parsers (which do not have a fixed lookahead) - and if you can create a parser for all other Perl constructs, I can parse the difference between s/// and s///e.