I think the confusing aspect of this is the fact that BootStrap 3 is a mobile first responsive system and fails to explain how this affects the col-xx-n hierarchy in that part of the Bootstrap documentation. This makes you wonder what happens on smaller devices if you choose a value for larger devices and makes you wonder if there is a need to specify multiple values. (You don't)
I would attempt to clarify this by stating that... Lower grain types (xs, sm) attempt retain layout appearance on smaller screens and larger types (md,lg) will display correctly only on larger screens but will wrap columns on smaller devices. The values quoted in previous examples refer to the threshold as which bootstrap degrades the appearance to fit the available screen estate.
What this means in practice is that if you make the columns col-xs-n then they will retain correct appearance even on very small screens, until the window drops to a size that is so restrictive that the page cannot be displayed correctly. This should mean that devices that have a width of 768px or less should show your table as you designed it rather than in degraded (single or wrapped column form). Obviously this still depends on the content of the columns and that's the whole point. If the page attempts to display multiple columns of large data, side by side on a small screen then the columns will naturally wrap in a horrible way if you did not account for it. Therefore, depending on the data within the columns you can decide the point at which the layout is sacificed to display the content adequately.
e.g. If your page contains three col-sm-n columns bootstrap would wrap the columns into rows when the page width drops below 992px. This means that the data is still visible but will require vertical scrolling to view it. If you do not want your layout to degrade, choose xs (as long as your data can be adequately displayed on a lower resolution device in three columns)
If the horizontal position of the data is important then you should try to choose lower granularity values to retain the visual nature. If the position is less important but the page must be visible on all devices then a higher value should be used.
If you choose col-lg-n then the columns will display correctly until the screen width drops below the xs threshold of 1200px.