You are sort of right. People who don't need visas to enter can be turned away if the agent believes their visit will be for the wrong reasons, such as being a "stay risk" who wants to immigrate rather than visit. People who show up with visas can be turned away if the agent believes the visa was obtained by lying (such as arranging a tourist visa but showing up with the tools you need to work.) See Does a US immigration officer really have the power to deny entry to the country at personal will?
People entering any country, even with the right visas, can be and are turned away if they have a criminal record in their own countries. It depends on the seriousness of the crime. For example Canada will not let you in if you have a drunk driving conviction. The USA, on the other hand, will - even if that conviction was in the USA. (Rob Ford coverage here in the Toronto area has made that clear.)
I can't quite tell if you put on your form that you might have a criminal conviction, or if when you got your paperwork back it said you might have a criminal conviction. If it's the latter case, you have nothing to worry about: they know about the petty theft and consider it too minor to exclude you.
I understand you don't want to fly all the way there for your urgent meeting and be turned away. You'd like some sort of paper reassurance to bring with you that says you'll be let in. The strongest reassurance there is is a visa, and you have it. This is as sure as you can be and while it's not 100%, you can't improve it. Take the flight, you will almost certainly get in.
