Using someone else node doesn't mean your coins belong to someone who run that node, but your coins are attached to someone else wallet. It's about privacy, not about ownership or fake/original coins.
The difference is, if you use someone else node, they will know your IP address, your address, how much your coins and every transactions you made.
Wallet apps and devices might just show numbers, but that doesn’t guarantee you actually hold Bitcoin.
Easy, just send your coins to someone else as small as you want, if you receive in other wallet/exchange, your Bitcoin is legit.