OK! Finally got the pics to load
So, normal opiate assays, probably like the one that the lab that the PO is using, really only look for morphine, codeine and heroin. They sometimes pick up semi-synthetic opiates like hydrocodone, but oxycodone doesn't have great cross reactivity with the assay. As you can see it is 35 times the cutoff needed, and if the lab is using a 2000 ng/ml cutoff, then a person taking oxycodone in therapeutic amounts won't screen positive (>280,000 ng/ml!)
So these companies that make screening assays make a specific oxycodone specific assay, which as you can see has a much better cross-reactivity so it can screen positives for people taking therapeutic levels, as well as abusers that aren't consuming vast amounts to get them over 280,000 ng/ml.
So the PO lab is probably only using a opiate assay and the doctor's lab is probably using both an opiate and oxycodone specific assay. If it is an issue with the PO you can ask if their lab has an oxycodone assay and if they could screen it for you. If isn't then you shouldn't need to worry, the reason you aren't screening positive in urine is because they aren't screening for oxycodone.