autoconf ignoring CFLAGS?

I'm building a package (vice 3.4) that uses GNU autoconf. Running ./configure fails with the following message:

checking size of time_t... 0
configure: error: can not figure type of time_t
error: Bad exit status from /var/tmp/rpm-tmp.wIgnPw (%build)

Examining config.log, this appears to be failing due to the following error:

/usr/bin/ld: /tmp/ccMTSdtB.o: relocation R_X86_64_32 against `.rodata.str1.1' can not be used when making a PIE object; recompile with -fPIC
/usr/bin/ld: final link failed: nonrepresentable section on output
collect2: error: ld returned 1 exit status

I tried resolving this by adding -fPIC to the CFLAGS environment variable:

CFLAGS=-fPIC ./configure

But while this is clearly being used during other stages of ./configure...

configure:3657: checking whether the C compiler works
configure:3679: gcc -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -D_GNU_SOURCE=1 -fPIC  -Wl,-z,relro -Wl,--as-needed  -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld conftest.c  >&5

It doesn't seem to be used in the feature tests related to time_t:

configure:9684: checking for time_t in time.h
configure:9700: gcc -c -g -O3 -Wall -Wformat -Wformat-signedness -Wshadow -Wpointer-arith -Wstrict-prototypes -Wuninitialized -Wunreachable-code -Wno-unused-parameter -Werror=implicit-function-declaration -Wfatal-errors  conftest.c >&5
[...]
configure:9753: checking size of time_t
configure:9758: gcc -o conftest -g -O3 -Wall -Wformat -Wformat-signedness -Wshadow -Wpointer-arith -Wstrict-prototypes -Wuninitialized -Wunreachable-code -Wno-unused-parameter -Werror=implicit-function-declaration -Wfatal-errors  -Wl,-z,relro -Wl,--as-needed  -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld conftest.c  >&5

Looking at configure.ac, the above code is generated from:

if test $bu_cv_decl_time_t_time_h = yes; then
  AC_CHECK_SIZEOF([time_t],[],[#include <time.h>])
else
  AC_CHECK_SIZEOF([time_t],[],[#include <sys/types.h>])
fi

I've been able to work around the problem by redefining CC instead:

CC="gcc -fPIC" ./configure

This works, but it's ugly (what if something wants to call gccwithout-fPIC?). Is there a reason that AC_CHECK_SIZEOF is ignoring CFLAGS?