Strictly speaking, the friend is correct here. I am reminded of a famous exchange from Shakespeare's Henry IV Part I:
Glendower: I can call the spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man; But will they come, when you do call for them?”
The distinction between purpose and result can be subtle but very important. The Sorcerer's apprentice cast a spell to animate one mop and bucket. But that wasn't the result.
In most contexts the difference will not be noted, as the intent will be obvious. But a resume is apt to be scrutinized closely, not just for what it says, but for how it says it, as a test of the applicant's communication skills. So I would write it to emphasize what you accomplished, not what you intended, and use "Developed a model that..." (not "and").
In response to a comment:
The reason I prefer "that" to "and" here is that "I did X and Y" indicates association, and possibly sequence, but not causation. It is a weak joining. "I went to the park and played basketball" probably means that the person played basketball in the park, but could mean he went to the park, swam there, then came home, then played basketball. "I went to school and texted Jo" was the texting done at school or after school? "Developed a model and identified..." does not make it clear that the model did the identifying, it may have been quite separate. The use of "that" makes the causative connection much more clear, which in a resume is important.
Where "that" does not work some other form must be found, it is not a bad idea to avoid excessive parallelism anyway. The other form might use "and" but if a stonger connection can be made it would be well to do so.