I believe (and please correct me if I'm wrong) that 'in jurul' is an imperfect translation of 'around'. 'around' means 'in the vicinity of' and also 'circling the circumference of', whereas 'in jurul' means "in the vicinity of' only. Both of them can mean 'approximately' I believe. So in this case, the sentence means "he swims NEAR the island" but NOT "he swims AROUND the circumference of the island". Right?
No. "În jurul" really means "circling the circumference" when associated with an action like "a merge / a alerga / a înota / a zbura”. "În jur" is indeed always "in the vicinity”. The articulated form ”în jurul” is also ”around” when associated with verbs like ”a se afla / a se găsi / a pluti”