Uneasy feeling about applicant

[Brandon Brown]

I hired a real-estate agent that we have worked with in the past to find us tenants. Recently we had an open house where we had a several potential applicants walk through and many seemed interested. One in particular though was asking questions that made me feel uneasy. Maybe I am overreacting but I feel like it could be some sort of scam.

The applicant first said they had already submitted an application without even seeing the place, this is not true because the real-estate agent would have told us. They mentioned that the place wasn't for them but a family member that was living out of town. The family member from out of town would have a second person living with them briefly to get settled in. Towards the end of the showing the person that was viewing the apartment said they want to avoid the non-refundable move-in fee and offered a two month security deposit with no interest. They were very adamant about trying to close the deal the day of the showing. The next day I get a phone call from a number I didn't recognize, it was the people that viewed the place before stating they never received an application from the real-estate agent and they were getting "nervous" because they really want the place. I never had my phone number listed and my real-estate agent did no give out my number so they obviously used public records to look it up. 

I want to believe they are just very impatient people and really liked the place but it was the first time something like this has happened to me and of course it is a bit unsettling. Has anything like this ever happened to anyone here before? Does this sound like a scam?