This is not an NEC issue. UL category GBYS says this:
Relocatable power taps are intended to be directly connected to a permanently installed branch circuit receptacle. Relocatable power taps are not intended to be series connected (daisy chained) to other relocatable power taps or to extension cords.
The NEC Section 110-3(B) requires " Listed or labeled equipment shall be installed and used in accordance with any instructions included in the listing or labeling."
The product you described are known as Relocatable Power Taps, and are evaluated to UL 1363. The scope of UL 1363 is available at http://ulstandardsinfonet.ul.com/scopes/1363.html. UL 1363 Section 1.8 clearly states "A cord-connected Relocatable Power Tap is not intended to be connected to another cord-connected Relocatable Power Tap."
Additionally, the UL Guide Information for Relocatable Power Taps (XBYS) states in part "Relocatable power taps are intended to be directly connected to a permanently installed branch circuit receptacle. Relocatable power taps are not intended to be series connected (daisy chained) to other relocatable power taps or to extension cords."