No approval from the district needed.

Question: The school district seems to give parents a hard time about 'approval' letters.....Is this within the law? I was under the understanding that all a parent needed was a receipt to verify they handed in the paperwork and that an approval letter was not necessary?

Right, no approval is required.

This is what the law and the Dept of Ed says:
This is point five on the http://www.pde.state.pa.us/home_education/site/default.asp page and then on the left, click on Starting a Home school program. I marked it in bold.

It follows that if an approval letter is not needed to begin the program, why would any other approval letters be needed, and the law again clearly states that if the superintendent believes homeschooling is not appropriate, then he takes action, they send a certified letter. the law is clear on that too. So if the ed is appropriate, there is NO action required as it is not stated in the law what the super is to do --as he has to do nothing.

5) Take the affidavit, education objectives, and medical records or doctor’s
notes to the Superintendent’s office in the school district where you live.
Superintendent’s office addresses are on the PDE
website,here: http://www.edna.ed.state.pa.us/
If you wish to mail the affidavit, send it certified with return receipt requested. Approval from the school district is not necessary to begin your home education program if the affidavit and proper attachments have been submitted to the Superintendent’s office.

This is right from the law, nothing about approval, AND only if belief that appropriate ed is not occurring can they ask for info and only via certified mail.

There is nothing saying they approve anything any time. Ask where in the law it says that the superintendent approves. This is what the law says:
In addition, if the superintendent has a reasonable belief that, at any time during the school year, appropriate education may not be occurring in the home education program, he may, by certified mail, return receipt requested, require documentation pertaining to the portfolio of records and materials required by subsection (e)(1) to be submitted to the district within fifteen (15) days; and documentation pertaining to subsection (e)(2) to be submitted to the district within thirty (30) days.