I know this is going to sound paranoid but I have worked in the field too long and seen to much to not be a little paranoid about the horrors children face ..... teaching children it is ok to keep a 'secret' puts them at risk of being abused by any other adult who will use that 'secret keeping' concept as a way to hide the abuse. I personally would have said 'dude its ok, you had an accident, it is nothing to be ashamed of and we need to tell mommy and daddy because we do not keep secrets at daycare!"

So yes I would discretely tell the parents what happened and explain to them 'he did not want me to tell you cause he seemed concerned he would get in trouble however we do not keep secrets at daycare and communication about things that happen here is important to keep open so I while I washed them to ease his mind about getting in trouble at home ~ just wanted you to be aware'.

My concern also would be what if the parents notice he is different underwear and question the kid ~ and he lies as to why ~ as many children will to avoid the perceived trouble they might get in for the truth ... and now you are dealing with them choosing to believe the kids word over yours 'after the fact' and the LIE of OMISSION is standing between you bending any trust they had toward believing their own kid

Or even if you put the clean ones back on thinking no harm no foul they will never know ~ what if the kid decides to say something about you having to wash the underwear afterall and put them back on so mommy and daddy would not find out .... what if the way he explains it does not SOUND good/right to the parent and they get a horrible gut feeling of why or wrong assumption about why that escalates into trouble for you with them accusing you of something ~ which this day in age sadly is quiet common for false accusations to be made on people

I just always prefer to be upfront and get ahead of the 8 ball with anything that might get 'twisted' as to what really happened .... so accidents in bathroom or bumps bruises and anything discipline related gets documented and shared with the parents to cover my ass!