must there be a story behind the pair?

This is actually a semantic question rather than a financial one. If you adopted a pure statistical approach with no consideration of the actual pairs, you would end up with hundreds or thousands of pairs, including some overlapping ones. Then we wouldn't call it a pairs-trading strategy but a long-short equity strategy.

The idea of pairs trading is you can get additional insight by considering specific reasons for the dependence between the stocks; and that insight can result in more accurate positioning, and also avoidance of big losses when the relation breaks.

Obvious relations, like two large-cap stocks in the same industry, tend not to be useful. That's confusing sometimes, because some of the famous early pairs trades involved such pairs, and they're still used for examples in most texts. But too many people are watching those spreads too closely to get the high Sharpe ratios you need for undiversified strategies like pairs trading. Leave those marginal Sharpes to the long-short equity people who have a lot more positions.

Also, when we talk about a reason for the pairs relation, we're talking about both a positive--why is it hard to imagine a world in which the values of these companies diverge from their historical proportions--and a negative--why do these stocks respond to different economic news? So for two near-identical companies the first question is easy, but the second is hard. For two seemingly unrelated companies like MS and EXPE it's the reverse. You might say something like, "In a good economy Morgan Stanley gets a lot of business and people travel a lot," but that's basically true of almost any two companies.

The classic pairs reason was two companies that responded to the same basic economic factors, say oil prices or interest rates or US dollar strength, but at different points in the supply chain, say crude oil prices versus gas station revenues. A single link is not good enough, virtually all companies respond to these factors. But you can find pairs that are matched on narrower factors, say fracking activity in the Northeast US or precipitation in central California, or that match direction on a number of broad factors. Or you can find two companies that are actually in similar businesses today, but that for historical reasons are listed in different sectors. Another common situation is two companies involved at different points of the lifecycle of durable assets; homebuilders and furniture stores with similar geography for example.

Anyway, when you have a reason, you have things to monitor to fine-tune your position; and to alert you if a big dislocation is a great trading opportunity or a sign than the historical relation has broken. If you don't have a reason, you'd better have a lot of diversification, meaning you can't afford the specific analysis work for each pair.