Well, it’s not so unlikely, is it? The Winns, according to Sally, hated Moth for being a ‘lazy’, non-driving, landless ‘townie’ and were totally against the relationship.
If they suspected it wasn’t in fact a ‘safe’ family holiday with Sally in her own room being chaperoned by the Walker parents, I suppose it’s perfectly possible they might call the Walkers’ house in a fit of heightened suspicion while they were supposedly all away. (Bear in mind that Sally says she’d never been away from her parents for more than a day…)
I mean, I think there were far more obvious parental reasons to think Moth/Tim was bad news than being a townie or having long hair. Even given the late 70s/early 80s’ general disregard for health and safety, by Sally’s own account he takes her climbing for the first time wearing unsuitable slippy trainers, and she lets go a rope to take a photo, meaning he falls off the rock and has to go to A and E! And on this famous trip to Scotland, he lands them on an exposed mountainside miles from a road in the middle of a dangerous storm in which they lose their tent and most of their belongings and could easily have died of exposure.
Even before you add in the fact that Sally is completely obsessed with him and will follow him into any unwise or dangerous situation, and that she says herself they frequently skipped college and work to be together, he’s not exactly any parents’ dream.