Mail problem with a domain

A customer is angry cause a person is sending him emails from a domain out from my server and some messages (not all of them) are bounced back.
I told him that he must ask the person who is sending the error he got.

I did a lookup to the mail address and turns back something like domain.dyndns.org
The whois of the domain tell me that is hosted in a hosting company, my doubt is why the emails have the dyndns.org mx, like if they are using a mx backup or something like that and why they dont use the smtp server of the domain itself.

Could this type services have problems with emails??

Thanks