Of course, they are likely to know your fields, because they could just look at the HTML of the form and read them off; also, if they're determined, they can fake the http_referer. There is a chapter on security in the PHP manual, including form-related issues.
There are a number of stunts you could try and pull to make sure a given form submission is valid in one way or another (depending on the particular circumstances), but the in the long run the short answer is that you should never trust data coming from the outside world to be entirely legitimate; it's just a matter of what level of paranoia you feel is justified.