MTUs go strange ways - ?

[lejeczek]

Hi guys

I thought there was no better place to ask but here so - 
both ends are centOS and end up having different MTUs for 
'wg' interfaces and that I thought, was wrong.
1370 (server) VS 1320 (client)
I expected that would be negotiated between nodes without 
user involved, right?
Moreover if I from the client do:

-> $ ping server -M do -s 1300
PING 10.3.3.1 (10.3.3.1) 1300(1328) bytes of data.
ping: local error: message too long, mtu=1320

Could some expert or two shed more light on what & why is 
happening?
many thanks, L.