Our local tv/telco/ISP lets us use a 3rd modem for the broadband only, but not if you go with VOIP or the TV box
I have two small caveats to use of a third-party box.
Firstly, when a new type of service is being rolled out, there is quite a lot of NRE to get the hardware ready. Without new hardware, there is no service. In this situation, I think it is reasonable to have a time-limited monopoly on the new hardware; the alternative is for the service to be priced to cover that NRE with the boxes thrown in "for free", and that doesn't actually help the consumer.
The above clearly does not apply when hardware to do the job is already on the market.
Secondly, isochronous transport - such as TV or VoIP - can be extremely sensitive to hardware; I've seen many phone systems that are sat behind the crappiest router known to man, and the customer bellyaches that his phone doesn't work. Swapping out the router for something of decent quality brings the system up ar expected. So whilst I wouldn't forbid third-party hardware for this sort of job, I would explain to customers that it would be their responsibility to choose something that works, with attendant charges for call-outs that end up being down to inappropriate customer-supplied hardware.
But these are minor quibbles; in general, customers should have the right to choose the kit they use.