Accept applicants with insufficient Service Animal docs?

I have been showing one of our rental properties, and received an application today.  This has historically been a difficult property to rent, and it has been vacant for 2 months, with no other qualified applicants at this time.

The applicants have 2 small "service dogs" with certificates from a random website.  The dogs are apparently 15 years old and only became "certified" a year ago.  We do allow for up to 2 pet dogs with additional pet rent and additional pet deposit.  The applicants are clearly qualified financially based on their application, and I conduct a thorough check on applicants.  Financially it probably makes sense to sign a lease with these applicants rather than leave the property vacant for an unknown period, even if it means not collecting pet rent or additional deposit.

My question is: Would you push the issue for the "service dogs" and make the applicants provide a letter from a medical professional?  There was no apparent disability (not blind, etc), and the dogs were not present at the time of the showing.  Is there any liability to not doing due-diligence and fully vetting the "service dogs" as being legitimate?