They should do more/better shopping for a mortgage. I just put their numbers assuming good but great credit, into Schwab Banks, mortgage calculator and they showed closing costs of $3900 for 280K loan (assuming 20% down. 2 years ago I paid $3600 in closing cost for $270K loan on a rental property in Vegas, via a mortgage broker so I know it's possible. My gut level is they should be able to get a mortgage for under $5K in closing costs. There are $1,000-$2,000 in closing costs, (Title insurance, escrow, doc fees) that you pay to buy a house mortgage or no mortgage.
Normally, I try and minimize the interest payments, in their case they should care about the interest rate since they won't have the loan very long, and instead focus on points 0-.25% points are possible, especially if they go with an adjustable.