Well! If you are talking about net safety of these websites then you can check their terms and conditions and their privacy policy. I am confident that they are not the ones who compromise your email address as their business model is based on finding who breached?
Plus why will they jeopardize their reputation?
Yes, their terms and conditions and what not ensure that the email address you input is safe, but what if they were hacked? What if they stored a list of the email addresses that were inputted there and a breach of security was done? Your email would basically be good as discovered. Credible or not, anything that's been used in the internet can't be removed no matter what, and once someone finds that little trace, you're as good as found. That's what probably @tranthidung is saying.
This is why you should really have multiple email accounts possible, depending on whatever usage you have for each one of them. It is simply an assumption ofc, nothing is for sure, but it's better to be safe than sorry no?