Responding as a School Psychologist and Supervisor of Special Education...
1. You respond as THE PARENT. If you read the instructions they ask you to respond with a "typical response" in mind. There is a "sometimes" option. Use that one for your example.
2. You don't ask for an IEP. You request an evaluation. Selective Mutism does not automatically require special education services. Your district will look at multiple data points and see whether or not there is substantial educational impact.
3. They will look at assessment results as well as answers to more qualitative questions. Is your child significantly behind? What else has been tried? What services will be provided through Special Education that are NOT accessible through other means?
Special Education doesn't "cost them more money". That's a huge misconception. In fact, students with IEP's bring money INTO a district. Also keep in mind that the success rate for IEP students is pretty damn crappy... I admit to that openly. Our graduation rate is poor and the labels stick.
If I was your school's Eligibility Chair, I would be looking for all other options to support an otherwise capable child who is experiencing an emotional/anxiety based disorder that is impacting her ability to express her understanding. Having an IEP with "Emotionally Disabled" as a classification has long-term ramifications that you can't imagine at this point.
Really really think this through. Your district is doing the right thing and you are seeing a very short-distance view of classification. Cost isn't a factor- you have been misinformed. The major factor here is that Special Education is for students who are educationally disabled and who cannot progress within the curriculum without specially designed instruction...
If I was in your shoes, I would be requesting a Section 504 accommodation plan that would include program modification, testing accommodations and school-based counseling.