Sort of I suppose. Difference being the 360 could be horizontal or vertical, and was designed to. The issues seen with disks were generally due to knocking or vibrations. XboxONE has been said to not support vertical standing atall, something to do with the slot loading drive.
Obviously its not an issue with slot loading drives in general as PS4\PS3 can do vertical.
Suppose I should add in an actual link. Although I read it on a different site initially.
http://news.cnet.com/8301-10805_3-5...the-xbox-one-vertical-do-so-at-your-own-risk/