Use of the Time-Turner to Help Sirius in PoA

[katgurl2k at yahoo.com]

No: HPFGUIDX 11669

Could someone maybe help me with this?  Harry and Hermione use the 
Time-Turner to go back three hours to help Sirius and Buckbeak 
escape.  The whole reason the original plan of takin Sirius and Peter 
to the Ministry did not work was because Lupin did not take his 
potion and he turned into a werewolf.  Wouldn't it have made more 
sense to go back to before they went to the Shrieking Shack and make 
sure that Lupin took his potion?  Then they would have been able to 
keep Peter and it would have been sorted out so that Harry could have 
gone to live with Sirius.  It doesn't make sense.