You're right, sorry.
Here are the interesting bits from the log, ran as you explained. If the rest is needed, you'll have to explain to me why can't I attach it...
9027.667821197:main thread: Writing pidfile /var/run/rsyslogd.pid.
9027.668012387:main thread: rsyslog 4.1.3 - called init()
9027.668030928:main thread: Unloading non-static modules.
9027.668047294:main thread: module lmnet NOT unloaded because it still has a refcount of 3
9027.668062299:main thread: Clearing templates.
9027.668103700:main thread: cfline: '$PrivDropToUser syslog'
9027.668378669:main thread: uid 101 obtained for user 'syslog'
9027.668396987:main thread: cfline: '$HUPisRestart on'
9027.668414288:main thread: cfline: '$ModLoad imudp # provides UDP syslog reception'
9027.668435038:main thread: Requested to load module 'imudp'
9027.668453094:main thread: loading module '/usr/local/lib/rsyslog/imudp.so'
9027.668518494:main thread: source file imudp.c requested reference for module 'lmnet', reference count now 4
9027.668543632:main thread: module of type 0 being loaded.
9027.668561301:main thread: cfline: '$ModLoad imtcp # provides TCP syslog reception and GSS-API (if compiled to support it)'
9027.668578222:main thread: Requested to load module 'imtcp'
9027.668594277:main thread: loading module '/usr/local/lib/rsyslog/imtcp.so'
9027.668648755:main thread: source file imtcp.c requested reference for module 'lmnet', reference count now 5
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9027.694032451:main queue:Reg/w0: main queue:Reg/w0: worker IDLE, waiting for work.
9037.921017509:imuxsock.c: Message from UNIX socket: #3
9037.921061887:imuxsock.c: logmsg: flags 4, pri 85, from '127', msg Jan 28 09:50:37 sudo: user : TTY=pts/3 ; PWD=/etc/rsyslog.d ; USER=root ; COMMAND=/bin/kill -HUP 20786
9037.921075867:imuxsock.c: Message has legacy syslog format.
9037.921095349:imuxsock.c: main queue: entry added, size now 1 entries
9037.921113124:imuxsock.c: wtpAdviseMaxWorkers signals busy
9037.921129786:imuxsock.c: main queue: EnqueueMsg advised worker start
9037.921194936:imuxsock.c: --------imuxsock calling select, active file descriptors (max 3): 3
9037.921222738:main queue:Reg/w0: main queue: entry deleted, state 0, size now 0 entries
BTW, on the stdout it actually says
rsyslogd: [origin software="rsyslogd" swVersion="4.1.3" x-pid="20786" x-info="http://www.rsyslog.com"] rsyslogd was HUPed, type 'lightweight'.