You're not using strict, so of course local our $p=Vars will work. It's just an assignment of a string to a package variable. Compare:
$ perl -ce'local our $p=Vars'
-e syntax OK
versus:
$ perl -Mstrict -ce'local our $p=Vars'
Bareword "Vars" not allowed while "strict subs" in use at -e line 1.
-e had compilation errors.
Also of interest:
$ perl -MO=Deparse -e'local our $p=Vars'
local $p = 'Vars';
-e syntax OK
perl -E'sub Monkey::do{say$_,for@_,do{($monkey=[caller(0)]->[3])=~s{::}{ }and$monkey}}"Monkey say"->Monkey::do'
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