Yes, travel insurance matters for a trip to Interlaken, and here the honest reason is activity rather than illness: this small town between Lake Thun and Lake Brienz has built its whole tourism economy around paragliding, canyoning, and skydiving off the surrounding Jungfrau peaks, and that is exactly where a routine policy quietly falls short. Swiss hospital care is reliably strong by any measure, so the real question is not whether you can get treated but whether your policy actually pays for the kind of rescue and repatriation an adventure-sports injury here can require.
Bern, roughly an hour away by road or rail, is the region's major referral hospital city, and anything beyond routine treatment in Interlaken typically means transfer there. What sets Switzerland apart is cost rather than distance: mountain and helicopter rescue in the Bernese Oberland is known to run expensive even by Swiss standards, and a policy that only covers modest emergency-transport benefits can leave a real gap if a paragliding or canyoning injury requires a helicopter lift out of a gorge or off a mountainside.
Paragliding tandem flights, canyoning descents, and via ferrata routes above town are the activities that draw most visitors to Interlaken, and they are also the ones most commonly excluded or capped by standard travel policies. Confirm your policy names these activities specifically rather than assuming a general adventure-sports clause covers all three, and check any altitude or descent-depth limit before booking through a local operator.
Keep the operator's incident report, any clinic paperwork, and receipts for treatment or rescue costs, since claims involving mountain rescue tend to need more documentation than an ordinary illness. Winter brings its own version of the same risk further off-piste, where avalanche danger applies to backcountry skiing outside marked runs, so check whether your policy covers off-piste travel if your visit extends into the snow season. Check whether your existing health cover extends abroad and specifically to Switzerland before assuming it applies here.