Earlier quoted context omitted.
You are contradicting yourself. It is scalable. It scales linearly (and for practical purposes indefinitely) with the amount of money you spend on AWS Lambda. It might not have a nice constant factor, but it is scalable.
This is just pedantic. Anything can be scalable using that definition. Heck, I could hire a 3rd world worker to manually draw the PDF's, scan them to PDF using a scanner, and put them on a server and it would "scale linearly with the amount of money I spend" on labor.
No, some things can't be, like badly architected monoliths, or databases. Especially with databases it's not a given, which is why for quite some time in the last years things like the "MongoDB is web scale" blew up and people started mindlessly asking "is it scalable" (which as you figured out, means very little for a lot of systems). I'm also pretty sure that your example scales worse than linearly, since you have to introduce multiple levels of management at some point.
"scalable" = "can it be scaled", which is not a given for every system