How they can claim this.
The ISP has control over your VDSL connection since the ISP is one end of the connection. They can determine if the problem is caused by the VDSL connection, for example because there are too much errors on the line etc.
Given that the modem is provided by the ISP they have often also some kind of access to it (depends on the ISP) and might get additional information from it, like the signal strength of the WiFi connections between your systems and the router.
If I don't change my modem they will see it?
It is unclear if you are allowed to change the modem in the first place. Even if you can they might refuse to provide deeper support if you use your own modem since they are unable to get some details to debug connectivity problems if they don't get access to the modem.
Anyway, they can at least find out if the problem is the DSL connection itself since they have control over this connection. They can find out if any problems with the DSL connectivity might be caused by the modem or by a bad line. If they don't find any problems with the DSL line they can conclude that any problems you report are likely originate on your site, i.e. bad WiFi connectivity or similar.
What else information then can get from my modem?
This depends on how much they manage the modem. In the worst case (full control of the modem) they might in theory have access to your internal network.
if I use a modem not provided by ISP, this will reduce the access?
Since it is unknown what level of access they have know (and what level of access they need to support you) it is unclear if the situation gets better if you buy your own modem. But if you choose the right modem you might get at least more visibility and more control of what your ISP can do.