What is legitimate or not is decided by the guidelines and rules that correspond to the conditions of the contract you signed. In the future, you have two choices: you can negotiate the contract, or you can try to get your manager to massage the system for you.
My previous job required me to wear a suit. Suits are generally not washer friendly. So I had to blow a fair bit of money each week on dry cleaning. I didn't expense report them. The company's stance was that dry cleaning, despite being required for maintaining my professional appearance for work, was my responsibility, and that I was paid enough to afford dry cleaning (I was).
Things like dress code, or conditions for sick leave (or bereavement leave, etc.) are generally laid out in the company regulations. If there is something you care greatly about, then you should bring it up early during the negotiations, otherwise you are tacitly agreeing to abide by the company rules (your contract probably explicitly says you have to do as told as well).
The absence of any restriction from filing an expense report for this does not mean that it is appropriate to do in the same way it wouldn't have been appropriate for me to expense my dry cleaning.
Now you can negotiate these things. If you absolutely must have a single can of Mountain Dew each morning on the company dime, you can request it be written in as a perk to your contract. Or you can accept an extra dollar a day in net pay to fuel your atomic green artificial coloring habit instead and have the same effect. Generally speaking people negotiate the real sticking points and ignore little stuff (like reimbursement for doctor's notes) for two reasons:
- There is no such thing as a perfect employment contract
- Requesting too much will likely hurt your pay and/or employment chances
Contracts are a balance where neither side gets everything they want, but hopefully both parties are satisfied enough with what they get that they are willing to compromise around the edges on both sides to maintain a healthy relationship.
The Easiest Way Out
Given that contracts are not perfect, and we all have our little pet issues that drive us nuts, most of us will come to an understanding with our manager. Perhaps the policy is no personal calls while at work, but your boss turns a blind eye to the call you get from your school when your child has a fever. And perhaps there is no flex time and the hours are 9-5, but because your child has a fever he allows you to leave early because you generally come in 15 minutes early, and it's just the right thing to do.
While your company may require a note to prove you are sick, you could always negotiate with your manager to see if (s)he's willing to turn a blind eye this time:
"Hey boss, I've got the flu and will be staying home today. To head to the doctor would be tough in my condition, and set me back $130. Is there any chance we could skip over that requirement this time?"
Your boss probably doesn't control your health plan, but (s)he probably has the ability to wave the requirement for the note. Being direct and honest about what you need at worst will get you a no, but it'll be a much easier path than trying to expense those costs (which will probably have to go through your boss and make it less likely to receive such favors in the future).