Rent collection - safe collection methods

[Kosh Vokter]

For making rent payment, tenant prefers to use Paypal with a business transfer (and not a person to person) option and Paypal charges a fee for that. To avoid that I suggested that they can make rent payments through direct bank deposit, which they are okay with.

Tenant said they can either do a wire transfer or ACH transfer.

Are there any downsides to giving the bank account # and having them make rent payments directly? I read on the forums, it's better to create a new account and provide that account # and immediacy transferring the amount to a different account once rent comes in, so as to not leave a balance. 

I don't have cozy or any other account.