I can answer from a Canadian perspective. Basically, in Canada, veterinary school is very competitive, more so than medical school in most cases (less spots available per number of applicants). The one university in Ontario with a DVM program requires that the Medical College Admission Test (MCAT) be written! Volunteer time in a vet's office is not only beneficial in most cases, but is also sometimes required before one can apply. Take the Atlantic Veterinary College for instance, there are standardized forms that must be filled out (sort of like a Letter of Recommendation) by a person with a Degree in Veterinary Medicine - in whose office you will have volunteered your time for a minimum period (set by the university). These are requirements that must be met before you are even considered, i.e. with these schools that I have mentioned, your application gets tossed out if this requirement has not been met.
You mention that the website says 20% of whether or not you get in depends on your experience. There's your answer, that's not a joke. They, like most schools, will likely have a scoring scenario in which 20% of your score deals with previous work experience (just like your grades, your interview, essays, letters of recommendation, etc, will have a fixed percentage of value on the application).
Essentially, since it is so competitive, you will have to look for a way to set yourself apart from everyone else. There is no such thing as a guaranteed acceptance and the highest grades mean squat if your essay sucks or you have no previous experience, etc.
It's a lot of work but if you have your goal in mind now then you are much better off.
I know all of this sounds discouraging, but it's not supposed to be easy or else everyone would have a degree in medicine (veterinary or otherwise). *insert cheesy 'you can do anything you set your mind to' line here*
I have done all of the volunteering years ago and have my letters of recommendation all tucked away ready for the application process - I'm getting my Master's degree first though, I start in a few months...
Best of luck to you.