I have never encountered a SMD part that needed to be hand soldered.
Probably what someone ran into is a part that needed a special profile such that the board would have had to be run thru the oven twice. If this is due to a single part, it could well have been more cost effective to run the board thru the normal process and hand solder the special part afterwards. It's not that it couldn't be reflow soldered, but that for that process in that situation it wasn't economical. I have seen this case a few times.
Another case I've seen a few times is when there are only a small number of parts on the bottom of the board. Two-sided reflow takes some special handling, and for a very small number of parts it's more cost effective to run the normal process for the top side, then add on the small number of bottom parts by hand.
More stuff is hand soldered than you might imagine in places where the labor rate is low. A factory one of my customers used in China had a whole manual assembly line right next to the more automated pick and place and reflow line.
Again, it is highly unlikely what you heard is due to a part needing to be hand soldered due just to the part itself. A assembler may have said they "need" to hand solder a particular part, but that was due to their process and tradeoffs, not inherent to the part.
Lead is a magic element that makes solder melt at a lower temperature and protects the tip of your iron against oxidization. Too bad it is a potent neurotoxin.
Most lead-free solders have high melting points. (Bismuth solder paste is lead free and has a lower melting point than leaded solder, but because it is a paste, using it with an iron is not very convenient.)
Without lead, and at higher temperatures, tip oxidization is your #1 problem.
That means shutting off your iron immediately when you aren't using it. Don't let it bake. Some fancy lead-free irons have an auto-setback that reduces the tip temperature when it is placed in the cradle.
And stay away from "CLEAN" solder! Water-soluble flux is very aggressive but corrosive! It will eat vias and traces if it is not immediately cleaned off (should be called "MUST CLEAN"). It is only used by industrial processes that include an ultrasonic bath after soldering.
"NO CLEAN" solder is what you want and means the flux is not corrosive and does not need to be cleaned. Yes, the terminology is confusing.
FWIW I like Kester Sn96.5/Ag3/Cu0.5. The fumes are no worse than lead solder.
Best Answer
60/40 solder melts at somewhere around 180 to 190 degrees Celsius, not 300-something.
Use a temperature-controlled soldering station.
In any case, the temperature in the device itself is not necessarily as high as it is at the joint being soldered. If you work quickly, you can create a fast, local temperature rise at the joint.
Also, depending on the size and geometry of the part being soldered, sometimes it is feasible to introduce a sink which removes heat somewhere along the pin between the joint and the part itself.