I been renting the same house for 5 yrs, I paid 2x amount of rent for deposit.

The prospective tenant has offered a pet deposit (it's illegal to require one in our jurisdiction).

His realtor claimed his relatives were paying rent - but being the inexperienced fool that I was at the time I never asked for proof of deposits or leases. 

@Seth Peterson I see it as a deposit.

He said it was completely baseless in law, however, he was concerned about future claims or even personal safety. 

Look, you can do a VOD (verification of Deposits) and have a loan approval I assume?

This means that in the event of a worst-case scenario, laws regarding rent increases, damage deposits, evictions, etc. are more likely to favor you the landlord. 

By budgeting $0 for any up-front repairs, you're banking on the best-case scenario happening and not leaving yourself any margin of safety in case a less-than-best-case scenario happens.I also see you've budgeted exactly 3.5% for the down-payment. 

Safety comes at a price.

Perhaps you can collect an additional deposit for utilities to raise your deposit monies.