Sounds fishy to me.
They are trying to get your personal information.
Red flag.
Do NOT click on any links, that are in that e-mail they sent you.
And do NOT fill out their "application" form. They will get your personal information that way.
Since you have never submitted your resume to anyone for the past 15 years, internet or not, they would not have your resume.
Nor would your Professor, if you have never given him your resume.
AND, it is proper protocol, that ANYONE who submits another person's resume to somewhere, they need to ask your permission first.
And your Professor had not said, that he gave your resume to anyone.
IF you have submitted your skill set, to any site, or are a member of any site that lists your skills set/experience (ie: sites like LinkedIn, or other networking sites), then MAYBE... they gave your information to a 3rd party site. Lots of websites, "sell" their member's data information, to 3rd party sites or Sponsors for money.
These sites that "buy" information, are called "Data Miners."
Or, to get to the bottom of it, you CALL that Hotel, (the HR department) and ask them HOW the heck they got your personal information and resume, being you NEVER submitted your resume to them, nor applied with them.
All of this, is very wrong.