We're using libcurl via PHP (I know, I know) which doesn't expose curl_global_init at all.
Here's the stacktrace for the /dev/urandom read -- it's happening in curl_easy_init.
Catchpoint 1 (call to syscall 'ioctl'), 0x0000003a74ecc4ba in tcgetattr () from /lib64/libc.so.6
(gdb) backtrace
#0 0x0000003a74ecc4ba in tcgetattr () from /lib64/libc.so.6
#1 0x0000003a74ec7a1c in isatty () from /lib64/libc.so.6
#2 0x0000003a74e60d51 in _IO_file_doallocate_internal () from /lib64/libc.so.6
#3 0x0000003a74e6d6dc in _IO_doallocbuf_internal () from /lib64/libc.so.6
#4 0x0000003a74e6ba7c in _IO_file_xsgetn_internal () from /lib64/libc.so.6
#5 0x0000003a74e61dd2 in fread () from /lib64/libc.so.6
#6 0x0000003341606414 in ares_init_options () from /usr/lib64/libcares.so.2
#7 0x0000003d3404f0c9 in ?? () from /usr/lib64/libcurl.so.4
#8 0x0000003d340242a5 in ?? () from /usr/lib64/libcurl.so.4
#9 0x0000003d3402f9a6 in curl_easy_init () from /usr/lib64/libcurl.so.4
#10 0x00002b35e0304fb0 in ?? () from /usr/lib64/php/modules/curl.so
#11 0x0000000000606da9 in ?? ()
#12 0x00000000006456b8 in execute_ex ()
#13 0x00000000005d2bba in zend_execute_scripts ()
#14 0x00000000005769ee in php_execute_script ()
#15 0x000000000067e44d in ?? ()
#16 0x000000000067ede8 in ?? ()
#17 0x0000003a74e1d994 in __libc_start_main () from /lib64/libc.so.6
#18 0x0000000000422b09 in _start ()
(gdb)
I just guess, but maybe the things missing in the stack trace (marked with ?? -- maybe you miss some debug symbols?) do what is described in the manual entry I've quoted (calling global init which calls ares?).
And why curl at all? PHP has built in HTTPRequest?
Here's the stacktrace for the /dev/urandom read -- it's happening in curl_easy_init.