"grep_cr" doesn't seem to suffer from this capturing.

Correct.

List::Util::any BLOCK LIST is syntactic sugar for List::Util::any sub BLOCK, LIST because of its prototype.

$ perl -Mv5.14 -MList::Util=any -e'say 0+any { $_ > 3 } 1..5'
1

$ perl -Mv5.14 -MList::Util=any -e'say 0+any sub { $_ > 3 }, 1..5'
1
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A sub's access to the variables of the lexical scope in which its defined is called capturing. (A sub that captures is called a closure.)

That's not the case for CORE::grep and CORE::any's blocks. Their blocks are no more subroutines than while's.

$ perl -MO=Concise,-exec -MList::Util=any -e'any { /x/ } @a'
1  <0> enter v
2  <;> nextstate(main 31 -e:1) v:{
3  <0> pushmark s
4  <$> anoncode[CV CODE] sRM
5  <#> gv[*a] s
6  <1> rv2av[t4] lKM/1
7  <#> gv[*any] s
8  <1> entersub[t5] vKS/TARG
9  <@> leave[1 ref] vKP/REFC
-e syntax OK
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$ perl -MO=Concise,-exec -e'grep { /x/ } @a'
1  <0> enter v
2  <;> nextstate(main 1 -e:1) v:{
3  <0> pushmark s
4  <#> gv[*a] s
5  <1> rv2av[t2] lKM/1
6  <@> grepstart K
7  <|> grepwhile(other->8)[t3] vK
8      <0> enter s
9      <;> nextstate(main 2 -e:1) v:{
a      </> match(/"x"/) s
b      <@> leave sKP
           goto 7
c  <@> leave[1 ref] vKP/REFC
-e syntax OK
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Note the anoncode (sub { }) in one, and the actual code of the block (match) in the other.