Assuming negative cash flow -Does it make sense?

[Michael C.]

I have an opportunity to assume a loan on a SFH for very low cost, maybe a few thousand in fees to transfer. The issue is that the property will not cash flow as a rental. If I can get the house for essentially free does it make sense?
2000ish build 3B3B SFH. current loan is at market value and around 6%.
PITI around $2,800. Long term Rent around $2,300.

Here are my thoughts: 

1 This is not a deal, cashflow is king.  Don’t buy a loser. Pass.

2 If the out of pocket costs are so low vs buying a comparable with 20% down both will be negative for +5 years anyway right? if I put $80k down to make $500 a month or lose $500 a month with no down payment until rents catch up to current market. It’s just a function of finance and Net Present Value. Either start $80k in the hole with +$6k cashflow or start $0 in the hole with -$6k cash flow. 
This also preserves my cash to still find more opportunities. 

What do you think, can I make a deal out of this? Which chain of thought makes sense here?