@Danny84,
Hello, Danny:
1. I am a very old man (75), so I feel more comfortable following the rules.
a. Therefore, I believe that your friend is "correct" when he insists on "That person is I."
2. First, may I disagree with your use of the word "object" to describe "me" or "I"? I believe that those pronouns do not qualify as an "object." I believe that most teachers prefer the word "complement." (An object is like "me" in "He helped me.")
3. Second, In 2013, I am pretty sure that 99.99% of Americans would say "That person is me." So -- in terms of the real world -- YOU are correct.
4. If you knock on someone's door, and someone inside asks, "Who is it?" how would you answer?
a. I assume that you would say, "It is me."
b. I assume that your friend would say, "It is I."
5. If you check your grammar books, they will probably agree that "It is I" is correct, but the newer ones will probably admit that nowadays "It is me" is acceptable. (Even on tests?)
6. Maybe it is only my imagination, but I can easily understand why "It is I" is correct.
a. "is" is often an elegant way to write the symbol =
b. It = I
c. I = It
d. On both sides, you need EQUALITY.
e. If you say "It is me," then you are saying "It = me." Right?
i. Following the "equality" rule, the other way would be "Me is it." Would you ever speak that way? Of course, not.
7. I have visited many grammar forums. All of them agree that nowadays almost all native speakers say something like: "Look at this photo. That person near the tree is me!"
a. Like you, I visit grammar forums in order to learn proper English. So it appears that nowadays "It is me" is proper English. In fact, I suspect that some people (who know the rules) avoid "It is I" because they do not want people to think that they are "showing off" their superior knowledge of grammar. And (ironically) if you do say "It is I," most people (who do not know the rule anyway) will respond: What's wrong with you? Don't you know that you should say "It is me"? (!!!)
James