This is a totally made up excuse (not uncommon these days). If your booking was through Kayak then NO credit would be due not just some of the nights. Reps need to be called on this and forced to do the research to find out what is happening and not just make things up to get you to go away.

As for number of nights, it does seem there are more and more issues with late check-ins and early check-outs. It's not really a system problem as it is merely doing simple date math and if you do/don't cross midnight then a day or tow off is technically the right answer. Howere, what is missing, in my view, is proper training to the property staff to adjust the dates based upon the situation. Some properties are better at this than others. Programmatically, they could add/subtract 12 hours before computing the dates, but MR IT is not going to catch that, or care. It's not up to them to fix the mistakes. Put them on the front line for a day/week, my guess hope is you might see great improvement.