Correct.
The "time.h" in the tools section: / hardware / tools / avr / avr / include / util / time.h
has "typedef uint32_t time_t;".
The Arduino Uno does not know "time_t" without including a library.
But when I select the Arduino Zero it does know the "time_t" 
The origin is std::time_t ? That is beyond my knowledge.
Then I found this:
#define _TIME_T_ long /* time() */
in ".arduino15/packages/arduino/tools/arm-none-eabi-gcc/4.8.3-2014q1/arm-none-eabi/include/machine/types.h"
It really does say a "long" :o because some functions return -1 when the date could not be solved. Ouch, we are in trouble for 2038.
Now I'm confused :