The 1-in-small-integer stat came from a study at 2 midwestern universities a few decades ago. Respondents (a 48% response rate, which indicates response bias would be present) were asked if they had, among other things, ever been attempted to be kissed when they did not desire it. 'Yes' responses were counted as sexual assault. So basically, if you were on a meh date and your date went for the kiss, but you backed out, these people lumped that right in with rape. I don't particularly blame the researchers, because they even cautioned that their survey had a lot of flaws and they weren't trying to measure rape prevalence.

Here's a source from the researchers themselves. To clarify a few points:

• They did not include failed attempts. The "if you were on a meh date and your date went for the kiss, but you backed out" situation you mentioned would not be counted in that statistic, nor would any attempted rape. Relevant quote:

Third, despite what has been said in some media reports, the 1-in-5 statistic does not include victims who experienced only sexual-assault incidents that were attempted but not completed. The survey does attempt to measure attempted sexual assaults, but only victims of completed incidents are included in the 1-in-5 statistic.

• Forced kissing and unwanted groping was counted as a separate category as "sexual battery", and the researches have always presented the statistic as such rather than saying they're referring to rapes. Since these are all completed incidents, cases not of the "he went in for a kiss and I backed away" type but the "he grabbed me and held me there and I couldn't get away" type, and are legally defined as sexual battery, I'd rather not throw them out entirely and act as if they're non-incidents. If you would like to see the statistics solely for forced penetration, though, the researchers explicitly calculated that (emphasis mine):

To limit the statistic to include rape only, meaning unwanted sexual penetration, the prevalence for senior undergraduate women drops to 14.3%, or 1 in 7 (again, limited to the two universities we studied).

There's a solid difference between 19% and 14%, definitely, but both numbers are pretty high. If I was to be convinced that this was an inflated epidemic not worth near this amount of attention, the numbers would have to be in the low single digits, probably. That's what I'd expect to hear if people are throwing away the 19% number as if it has no value. If it's actually 1 in 7 women being forcibly penetrated against their will instead of 1 in 5... that doesn't help me sleep much easier at night.