If you owe money on a vehicle, you are not going to have a 'Title', just a registration. But if you do own it outright you will then have a 'title' and will have to produce it.
How do they know that you own it? In some states your registration may give you away because it has a place for the 'Legal Owner' and the 'Registered Owner'. If both say you, or one says 'same as' the other, then that indicates that you own the vehicle and will need to have the 'Title'. Other states registration does not have the legal and registered boxes, so you don't really need to carry the title with you.
Oh, and if you don't own the vehicle, and they know this, you will have to produce a letter, on company letterhead, giving the VIN and the dates you plan on being in Mexico, and notarized, that gives you permission to take the vehicle into Mexico.
Hope this helps