Yes, my Dad was the same way with my Mom and would even "hide" things just so we wouldn't know what was happening with her. Of course we noticed! Neither of them wanted someone around all the time, but when my Dad became too feeble to take care of both of them and the household duties, we needed to step in and make the decision. Sometimes you have to watch out for the caretaker as well -- even though they state things are okay with them. This age group is a stubborn bunch, but that's how they made it through so many situations throughout their lives.
Your parents are so fortunate to have you next door...I was about 10 minutes away, but it was tough to have to hold down a full time job, family, and take care of all their medical appointments, housekeeping, etc. So it just made sense for us to get some help. My siblings are all 3 hours away and they would help when they could, but it's just a tough situation. Take care, and keep sharing! And, so glad you are going to support groups. That's a great thing!