and in my experience, even the loosest cloth will allow draw if the cue ball is close to the object ball.
In most of my experiences, I would agree with you Bob. However the cloth on my personal table was actually loose enough to give me only a foot maybe two of draw, and I have an up and down the table draw stroke on it after stretching it tight. If he can draw fine at the pool hall but not at home, The only logical thing in my mind is the cloth... maybe even worse than mine was... unless his object balls are very very light weight; like the ones that come with those 4 foot pool/foosball/ping pong kids tables.
A bar near my house replaced a broken 2 ball with a super light plastic ball, and with a straight in draw shot, the cue ball rolls forward a couple feet before coming back 6 inches lol.
Well the OP has a few things to check and get back to us, I'm more than curious now.