ok( ThatPackage::blah $foo, 'blah' ); 
means 
ok( ThatPackage::blah($foo, 'blah') );
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Update: I wrote the below, obviously after reading ikegami's answer above. Yet, I went on, totally wrong. The only problem with his answer was that it's a bit terse. When the sub you are calling eats the rest of the argument list, you get surprises. For example, look at print. It seems a litle silly that ok() is OK with only one argument, but it is, which hides the real problem in your code.
sorry for confusing... (e.g.:disregard the rest of this post)

It is not possible to explain the semantics of your code without access to the definition of ThatPackage. If you could include that definition, we could probably better explain what happens and why.

For example, include your definition of ThatPackage::blah something like this (after verifying that it still demonstrates the problem):

use Test::More 'no_plan';
#require 'some_file_with_my_functions.pm';
package ThatPackage;
sub blah { return $_[0] =~ /hi/ }; # Does NOT demonstrate the problem

package main;

my $foo = "hi";
my $bar = " hi";

ok( ThatPackage::blah $foo, 'blah' );
ok( ThatPackage::blah $bar, 'blah2' );

ok( ThatPackage::blah($foo), 'blah3' );
ok( ThatPackage::blah($bar), 'blah4' );
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cheers

Fair enough, here it all is, shortened as short as possible:

Contents of MyFile.pm

#!/usr/bin/env perl
use warnings;
use strict;
use feature ':5.10';

package ThatPackage;

sub parse { } # Yep, even empty the error occurs, because it never eve
+n gets as far as calling it
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Contents of unit_test.pl

#!/usr/bin/env perl -w
use feature ':5.10';
use Test::More 'no_plan';

require 'MyFile.pm';
my $foo = "blah";
my $bar = " blah";

ok( ThatPackage::parse $foo, " this is a test" ); # fine, test doesn't
+ pass but runs fine
ok( ThatPackage::parse($bar), " this is a test" ); # also fine
ok( ThatPackage::parse $bar, " this is a test" ); # error here: 'Can't
+ call method "ThatPackage::parse" without a package or object referen
+ce at unit_test.pl line 43.'
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