Phone download mode showing 'custom' status means something has done to it, whether it's root, or any other modification.
The international manufacturers ALWAYS reply within 1-2 days, if your question is legit. That check is only for factory refurbished phones, not for unprofessionally repaired/refurbished sets.
On the box, there will be website mentioned for specific country for which phone was released initially, use 'contact us'. It asks for device serial number, but I included IMEI and photo of phone back label and box label too.
Phone info is very useful, but it can be modified too to show different specs and info etc, but factory resetting phone and then installing stock rom via Odin will bring the true colours!.
But the charger connect and earphones correct count is part of EFS and only a 'retarded monkey' would tamper EFS to reset them. They are never tampered, but count upto 10 is acceptable even for brand new phones, i confirmed from the manufacturers.
Stock/custom rom or recovery has not much link with it in most cases, unless EFS gets lost or corrupt.
If I change the model number, variant or imei (EFS tampering). Imei check will reveal this tampering. OLX has some of these phones, like me and my friend checked some OPPO Find 7 which turned out to be a Chinese clone of it and imei check figured it out and we later confirmed by matching specs. So in all cases we had, it showed correct info.
So, anything is possible and nothing is absolutely foolproof!. But they help a lot.