Water pooled on roof

This video shows water still pooled on the roof after the rain a couple of days ago. I talked to the guy from Dynamic Roofing who was up there to do our 3-year maintenance. He said this is normal for a flat roof (even the larger pool on the SE corner). He agreed it's questionable whether we needed to have the gutters installed a few years ago, given the building was designed in 1974 to be gutterless, and it has been fine for almost 50 years without them. He pointed to the large USF dorm to our east that has no gutters. Regarding adding a bigger downspout, he didn't think it's necessary. I asked them to fix anything that could come up during our structural inspection. He pointed to the seals around some of the vents and other things sticking out of the roof that's cracking slightly and showing some age. He's going to reseal around those things.