Re: Pronoun police
Taking "company" as a collective noun (the company is the collection of those who have investments in it) we can turn to Fowler* for advice. The advice there is that consistency is essential but either usage is acceptable. So you and your friend can both be right.
Fowler falls foul of Muphry's law in giving an example of incorrect usage:
"The government is pressing ahead with their policy or privatization"
Note the "or".
* Yes, I have a copy tucked away in the "Misc user guides" folder on my desktop. Why do you ask?