Can I not implement my own submission mechanism (with my own web server and rest server on the other end) to receive submission data?

On  the  FAQ  it  says:  "To submit PDF forms, you need to use software such as Adobe Acrobat Reader."  

Why  do  I  need  Acrobat  Reader,  can  I  not  implement   my  own  submission  mechanism(my  own  web  server  and  rest  server  on  the  other  end)  to  receive  the  submitted  form...?

On  the  FAQ  it  says:  "To submit PDF forms, you need to use software such as Adobe Acrobat Reader." Why  do  I  need  Acrobat  Reader

I'm not sure how this is relevant to your original post. Did you get this snippet from our guide about Fillable PDFs? If you did, then you won't need a reader at all. This only applies to users who convert their online JotForm forms > into a fillable PDF form.

Can  I  not  implement   my  own  submission  mechanism(my  own  web  server  and  rest  server  on  the  other  end)  to  receive  the  submitted  form...?

All data goes to your account's SUBMISSIONS PAGE by default. Each form has its own respective submissions page.

Complete guide: How-to-View-Form-Submissions

If your intention is to handle the data yourself using your own rest web server, you can use our API for that. And I'll be discussing how that can be done on this next thread.