This poster is being sarcastic - it was actually the OP's doctor that was surprised that her children didn't get sick (in geberal ie colds/flu etc) more often because they didn't have their vaccines. Everyone here knows vaccines do not prevent the common cold.
Your initial premise is inaccurate - vaccines do not prevent colds. Vaccines are very specifically targeted against specific viruses, and will not keep you from infection with all the other viruses out there. There are no commercial vaccines against the common upper respiratory viruses. You would need 200+ different vaccines to cover the known causes (I cringe at the thought of THAT syringefull)