It comes down to semantics. Yes the other person was being picky. Yes what you were doing is not the best practice. No, what you're doing is not WRONG technically, but you can ADD VALUE to the content by using the ordered list.
Since Ordered List is a tag, it is by definition machine-readable, without any special parsing. Using just 1. 2. etc as plain text embedded withing Paragraph content is not immediately exposed to whatever machine readers / code / other automation might want to work with your content.
The OL identifies that section of your content as an ordered list. That's adding (a little) value to the content because now it's providing a little bit of meta-data about what KIND of content it is. It's a numbered list.
I know, you're saying so what?
Well, let's suppose this content is being "read" by a blind person using a text reader software, where the computer reads the HTML page, parses the content and then speaks it to the user. The user may have enabled a setting saying - okay, for every ordered list, i want you to read me one item at a time and then pause and wait for me to say "next". Or whatever - just an arbitrary example.
Basically, by providing additional (semantic) information about your content, you are enabling software, devices and other processes to work with your content in more meaningful, contextual ways.