Good (or morning afternoon evening night)

emacs -Q:

;; OK
(with-temp-buffer
   (looking-at "^"))
t
;; OK
(with-temp-buffer
   (looking-back "^"))
t
;; Bad: endless loop
(with-temp-buffer
   (require 'thingatpt)
   (thing-at-point-looking-at "^"))

In GNU Emacs 25.1.50.1 (x86_64-pc-linux-gnu, GTK+ Version 2.24.29)
Repository revision: 27d343070d02210316e69e4f7da1faeea2d87608