Baloney. Most of the LED spec sheets I have seen, do specify a pulse current. Typically, they will tell you the max current for a 10% duty cycle. Here is one:
https://cdn-shop.adafruit.com/datasheets/WP7113SRD-D.pdf
See "Peak Forward Current [1]" in "Absolute Maximum Ratings".
"Notes: 1. 1/10 Duty Cycle, 0.1ms Pulse Width."
You haven't given any details or even mentioned how the LED is driven from the Arduino. I really hope you have some drive circuit and not just connected it directly to an output pin.