Your friend's explanation has its source in the Gemara Pesachim 8a. "Rava says: A courtyard does not need to be checked for chametz since crows are to be found there." This is the accepted Halachah.
You are right in that your lawn is your property/domain. It is true that one may not keep chametz there over Pesach, just like the house. However, we need some understanding of why we check our homes in the first place. We can then see the difference when it comes to lawns that do not need checking (as well as why we empty birdfeeders anyway).
Earlier, the Gemara on 6b explains that when we search, we need to nullify the chametz (declare it ownerless and like dirt) as well. The Gemara asks why? If its about crumbs, who cares? They are not worth anything anyway and need no nullification at all. So we say that maybe (by accident on Pesach) we will find a "gluska yaffa", (nice piece of cake or challah) and want to keep it even for a moment. So we need to nullify it all beforehand, so that at the moment you find it, it is already nullified. (Rashi)
However, it is obvious that larger amounts of chametz (greater in size than a stray gluska yaffa) will be removed or sold beforehand. Those things won't be missed easily. It is the random garlic nut that fell behind the couch which we are searching for with a candle. :)
Therefore, in your backyard, you can rely that such random morsels of goodness will be quickly eaten by birds. But, a large sack of chametz flour left in the backyard, still needs to be removed or sold! You need to look around the backyard (without a candle and feather) for such items (unless you never put stuff like that there all year anyway).
That is why birdfeeders need to be cleaned out (if you use chametz feed). You are not checking a crack in the bird feeder that may contain unknown chametz by candlelight. The bird knows how to do that for you. :) But you did deposit a large blob of chametz into the feeder yesterday (too much for the birds to finish off that fast) so you need to go back and throw it out.
Another reason some people strictly remove even small crumbs of chametz (its a chumra), is because the crumbs may find their way into food in the kitchen or a cheerio may get into a child's mouth if they find it on the floor. Chametz, even in a minute amount is not "batel" even 1000:1 if it falls into food on Pesach. So there is an extra stringency to clean such crumbs found in the kitchen/diningroom area. However, we can assume that crumbs in your lawn will become disgusting and not make it to the kitchen anyway, even by accident.
I hope this helps. :)
