Not a particularly great answer, let's try something else;
Short the answer to your questions really has to do with what transformers are used for in an antenna system. Some kinds of transformers change an unbalanced feed (those that use coax cable, for example) to a balanced feed (think of ladder line). Others are used to isolate the antenna from the feedline (very useful in transmitting applications), change one impedance to another or even isolate noise producing currents off a feedline.
This is a very broad description, and whole books of theory have been written on this subject. These are not just for wire antennas - there are various kinds of amateur verticals, and even some beams, that use transformers (of one kind or another - there are MANY types).
When talking about transformers, don't mix 'antenna' and 'receiver' - there are specific types for each, and each has a very different function. A 'receiver' transformer is most likely to be thought of as being part of the power supply, and has nothing to do with the RF characteristics of an antenna.
Mike