I dont use Business Catalyst.
I have been running some of these same sites on hostgator for years using Dreamweavers FTP and NEVER had a problem. This is exclusive with Dreamweaver CS6 and I'm not the only one having the problem either.
And yes it is possible that Dreamweaver is changing the permissions or something in your promgram is.
I was even on with your India Adobe support doing a screen share and they watched in real time as I uploaded a file and Dreamweaver and it changed the permissions to 000. You can 'Get' a file with 775 permissions then 'Put' that same file and it will chanve to 000 permissions.
If I use Dreamweaver CS5.5 NO ISSUES.
No one has addressed this problem with CD6 or called back as promised from support.