That info is almost completely wrong. You have to be patient against Falco. I'm not going to give a whole guide now, but I'll mention a couple of things.
1. Typical thing they do at the start of the match is start shining. Grab an armour piece, and guess what you do? No you don't throw it. You jump up and forward B his *** while he's trying to reflect.
Then, I usually throw the piece after he gets hit. Usually after you throw a piece against him, you should start shielding in case it is reflected.
2. Down B escapes his chain grab instantly.
3. Like Cake said, crawl under lasers. Space with D-tilt while crawling when you get close. Don't just crawl right into him, mindgame crawling back and forth and try to get up when you have the opportunity.
4. Down B attack will hit him out of his Phantasm (side B). This is a very useful edgeguard if you anticipate it right. You can also go for your side B if you're fast enough to hit him before he phantasms, or if you expect him to recover in another way.
Edit: I actually just saw a vid by Sparrow that had two more ways to edgeguard the Phantasm when Falco goes for the stage. He downsmashed him out of it as well as hit him with a paralyser shot. I haven't thought of this before for some reason. Paralyser seems more accurate, since you're likely to actually hit with it. If you can space yourself far enough then d-smash is the better set up though.
I disagree about the D-smash chain though. It hardly works really. The most I can get against someone with good DI is two double d-smashes at 0%, or if the D-smash is degenerated, then three doubles at 0%. Both obviously go into a combo of your choice, and can be a nice damage racker. However, you shouldn't really go crazy trying to pull one off, since you'll often take too much damage yourself that way.
