second study show minimal apnea

I would check the details of the first part of the split study. How much time was recorded while supine AND in REM. I've had a couple studies where the doctor noted that the test was "technically suboptimal" due to not capturing that oft worst case scenario. If your test happened to be like that, you could argue the case that it is not fully reflective of your condition.

Are there not two sets of data for the split-night study? In other words separate AHI, snore, O2 levels and arousal numbers for the first part of the night and then for the titration phase?

Yes the numbers on the treatment phase are.
total events 0
arousals 12
Lowest Desat 91
Average Sa02 90.7

The Sa02 is def better with the mask on

If the criteria was not met for the split night study, then they should not have done it. This the OWE you a full night diagnosis study. I would go back to the doctor or the lab and pursue this. Their mistake is costing you your treatment and your health. It will be cheaper for them to give you a full night diagnosis study than to deal with a lawsuit because you drove and got in accident because of their mistaken diagnosis. Remind them of this.

I agree to definitely pursue this with the doctor's office, especially considering its likely a new machine would be denied based on this (untreated AHI under 5). Also note that for AHI between 5 and 14 you typically need to have apnea symptoms or related conditions for them to cover CPAP (otherwise an AHI of 15 is required). Knowing your insurance's specific policy on this would be good, although I assume you'll know soon enough with either an approval or denial.

Besides the previously mentioned points that a titration shouldn't have been done if you didn't meet the criteria, and getting supine vs. non-supine info (for example if you only had significant apnea on your back before and for the new study you were on your side the whole time), also see if you even got REM sleep during the diagnostic phase of the new study (and compare that to your previous number of events in REM vs. non-REM, as many folks are significantly worse during REM). The total diagnostic recording time was quite lower than the earlier study (3 vs. 7.5 hours), such that for many folks they wouldn't even reach REM or at least not a significant amount of REM in that time. In my opinion they should give you a full night diagnostic study without an additional cost.

I can give myself as an example. I had a diagnostic study about 18 months before the one which diagnosed apnea. In that original study I was just below the AHI=5 cutoff. I think a contributing factor to that was my fragmented sleep, with which very little REM was recorded. My later two diagnostic studies showed I was much worse off in REM (and I would have still been just under an AHI of 5 if only non-REM was considered for those).

Hopefully someone else can comment on the oxygen reading, but from what I know, even your average O2 with CPAP was low, although I've heard of much worse. I'd ask your doctor specifically about that. They could for example order an oximeter study over several nights. That low O2 data from the study may help your doctor substantiate an appeal if they did decide to do that without redoing the sleep study (assuming insurance denies a new CPAP). Best wishes.