Does this car deal sound fishy, scam maybe? PLease help Honda Civic EX Coupe 2002

Is this car a lemon or a scam honda civic ex coupe 2002
Well long story, I just went to check this silver honda civic ex coupe year 2002 with 78k mileage. The kbb value is a few hundred above their selling value. Sell Price is at 7800
kbb fair condition value is at 8100 and good condition value is at 9000.
The carfax report is clean.

The car looks fresh, paint looks mint 9/10, inside looks great 8/10.
The problem is here, the car has no plate. The owner said her father (the name on the title) brought her a new car by surpise for her birthday. So she just swtich the plate from the civic to her new car at the DMV. On the day I went to see the car(yesterday), she told me I can bring it to a mechanic shop(she going to switch her plate back on)

Today she said her father refuse, saying that the car is still under her father name and if anything goes wrong, he will be in a mess. Later today I call her saying there is a mechanic shop only 5-6 blocks away. She still give me the same story no.

Another problem is shes not going to be there tomorrow (cuz work) but her boyfriend will do the talk and deal. She did said if i want the car, her boyfriend will call her father to come and sign the title over.

So now I am left with a choice of bringing a mechanic over to check the car and can only test drive within a block away from her house.

Is it a really big deal if I can't test drive a used car in the highway?
Since my test car range is only 1 block.

Does this sound fishy to anyone maybe a scam or the car has hidden problems?

Can a mechanic check the car for all/most major problems by just going there in person? another question is will the mechanic be able to check all the problem as if the car was brought to his shop?

Also she said her aunt brought it from honda dealer used certified and sell it to her for cheaper. The carfax report said the car was leased to first owner and sell as certified used car to second owner, which fits what she said.

I lived in New York City. PLease help me out guys.