No, they didn’t break it, but they sure did a good job at frustrating me to no end until I realized what was going on.
When setting up a gmail account you are giving two options “email only” or “email, contacts and calendar.” If you select the email contact and cal, you get to select push. If you select email only it sets it up smtp, which only gives you “every 15 minutes.”
For some accounts I didn’t need contacts or cal, so I naturally selected “email only.” My tip to you, select the second option and just leave contacts and cal unchecked and all will be well.
Happy land continues!