Confused on vaccine timing

My puppy will be 16 weeks old Wednesday. He had his last parvo/lepto shots a week ago at 14.5 weeks old. He still needs his rabies shot.

I had originally scheduled him to get the rabies shot a week from today at 16.5 weeks mostly just to space out visits and shots. But in speaking with the vet this morning, they said he has to gave rabies before he can be around other dogs – which is a challenge since he starts his next training this weeknd (he already finished puppy class) and we want to start taking him places on his feet since he's nearly too big for his stroller.

So my question- the vet said if he gets his rabies shot this week, come this weekend he's basically good to go since he's 2 weeks past parvo/lepto and will have had his rabies shot.

Everything i am reading online says 28 days for full vaccination, but also dog to dog rabies transmission seems low. My vet is advising he'll be fine to socialize in 1-2 days after his rabies vaccine.

Am I overthinking it or is this advice concerning?