Your description of how our works is subtly wrong. The following demonstrates this, without any strict in the way.

package foo;
our $foo = "I'm in foo";

package bar;
our $foo = "I'm in bar";

package foo;
print "1) $foo\n2) $foo::foo\n3) $bar::foo\n";
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Note that our caused you to access $bar::foo even when you'd have otherwise expected to access $foo::foo.

For giggles and grins, mix our with $_ when you aren't in package main. Tons of confusion!