The casting into combat rules seem pretty crystal clear to me.
"Wizards cannot cast spells at units engaged in close combat unless the spell only affects the caster himself or the spell's description specifies otherwise." BRB pg 107.
Rule of Burning Iron is a spell that had been argued about for quite some time about the ability to cast it into combat (or even into games on the neighboring table). I'm actually rather relieved that they got around to answering this one finally. The reason that there is an exception on this spell is the spell specifically states "
No targeting restrictions apply except that the wizard needs line of sight to the target." It seems clear that GW has ruled that a spell not being able to be cast into combat is a targeting restriction and would be included in the catch-all phrase of no targeting restrictions apply.
I don't believe that tree singing states anywhere that it ignores all targeting restrictions. Simply having no requirements for range or line of sight doesn't mean that it completely ignores any and all other restrictions altogether. Even a spell like, say, foot of Gork which states that it stomps "any one enemy unit on the table" may not be cast on units in close combat because it isn't specified in the spell description.