The first thing to understand is that Month + Day + DayOfWeek does not mean anything to the Calendar. The Calendar will calculate the true value of the date based on
YEAR + MONTH + DATE
or
YEAR + MONTH + WEEK_OF_MONTH + DAY_OF_WEEK
(Or some other combos like year + day of year etc.) So Date + DayOfWeek doesn't inherently mean much to it.
The second thing to understand is when you set on a Java Calendar it doesn't actually recompute the absolute time or update related fields until an operation that forces computation occurs.
After your first set, the calendar is in a conflicted state. The month and day say that it's July 12th, but the 'week of month' and 'day of week' still say that it's today, whatever today is. You then call set day of week to friday. So now year month and day say July 12th, but the 'week of month' and 'day of week' fields say it's Friday of 'this' week.
The rules of the calendar say that the most recently set field "wins" when there's a conflict, so the week of month and day of week combining to say Friday of this week are what's used to calculate the other fields.
Inserting a get in the middle 'fixes' it because it forces the entire internal state of the calendar to get recomputed to Tuesday July 12th before setting to Friday, so there are no internal conflicts. The 'week of month' got set to the week that contains July 12th by the recalculation prior to you setting day of week to Friday.
Edit: Sorry to make changes after two days, noticed this open in an old browser tab and thought I would expand for the hopeful help of future googlers:
The reason it worked for Jon in the comments is he lives in London. His computer thinks weeks start on Mondays. So when asked for Friday of 'this' week, it still responded July 15th when asked on Sunday July 17th. I bring this up because differing first days of the week in different Locales are just yet another way that trying to use the WEEK_OF fields in a calendar goes haywire.