Hi John!
Yes, some of the stories are true :-0
From the 23rd till the 1st, it's incredibly busy at Disney World. From experience visiting around this time in years past, the 24th, 25th, 26th, 30th, 31st, and the 1st are your busiest times. The 27th-29th are also busy, but not so much as the aforementioned. Those are the days you may want to try Magic Kingdom, easily the most popular theme park for guests.
My recommendation is to get to the parks early. Also, take advantage of any early Extra Magic Hours at the Parks. Starting around lunch time and beyond at the Parks, however, you'll see the crowds start to really pick up.
So, you may have to weigh what may be best for you. Once I set the expectation that me and my family will be dealing with large crowds at Disney sometimes, it makes it just a little bit easier to swallow :-)
Have fun!