We don't homeschool, and our children are enrolled full-time in private schools, but they are also enrolled in a public independent school program that's available to homeschool and private school families in our state. As Dude mentioned, these programs are going to vary from state to state and possibly school district to school district, but hearing how other programs work might give you ideas to use when you talk to your program's staff.
Also, fwiw, it's possible that you might just have been assigned a very nit-picky grouchy teacher/staff person you're working with, so one thing you can do is to try to look for another contact in your program to call and discuss your concerns with.
This is how our program works:
Work samples: we have a certain # of work samples we are required to turn in for core classes such as Math, Language Arts, History, Science, etc. We can either turn in originals and ask that they be returned (if we want them back) or we can scan in the work and email it to the teacher.
PE - any type of organized sports, sports class counts to PE hours as well as simply putting together an individual sports plan and keeping a personal log of activity and time. The instructors our kids have are actually *very* willing to sign forms to show that our kids attended their classes on (whatever) dates etc. In our area, we are reimbursed for expenses as part of the program, and quite a few families in the program use their funds to pay for things like dance, gymnastics, soccer, as well as Kumon, Sylvan etc - so the instructors at these places are more than willing to sign our forms simply because it is good business and makes it possible to have students attend whose families might not otherwise be able to afford the lessons. We can also take pictures of the kids doing their sports, and I've also sometimes had my kids do health-type research projects as part of their PE work "samples".
Music - my children get credit for weekly piano lessons and piano practice. Our teacher has no issues with signing our forms.
For the forms for PE, music, etc - (i.e., non core classes) - the majority of the form has to be filled out by the parent (description of the activity, when the child attended etc)... so it's not a huge hassle to give it to an instructor and ask them to verify. We also have our receipts for sports/music/art classes that we can show as proof our students participated.
State testing - our kids are required to take the state tests each year, same tests they would take if they were enrolled FT in public school.
JMO, but I think it's reasonable for the program representative to require something more than a guarantee from you that your child has done work even if it's work you're only requiring verbal discussion/responses for as part of your curriculum. Our program would let you be creative in how you showed this type of work - you could record a discussion or question-answer session to turn in, or you could scribe... just think it through, come up with some way to show what your child has learned.
Do you know any other parents who've participated in this ISP? I found it helpful talking to other parents in our program to get ideas on how they handled grading/reporting/etc. It does take a bit of time for planning and administration (paperwork) on my part.
Best wishes,
polarbear