Some companies holding small in-house team and taking outsourced as backup/help group. So that's also something you may consider as an start up.

In my opinion, the fact that they are getting the service is good enough, however customers should have the right to know whether its in-house or not.

That seems kind of like a so-so answer, like your customers should be happy they are getting any support at all. Sorry but I disagree and that is not the stance I take. All clients no matter if you in house staff or outsource should always be provided a quality level of support, not just "good enough" support.

we used to use outsourced support, but when we did client feedbacks it was clear clients were not happy as they were treat like numbers and not paying clients, so noy all support is in house.
we have a stance that if client A is paying a £1 a month and client B is paying £30 a month then why should the support they receive be different, they are both paying clients at the end of the day

Any little edge you can offer helps build a solid customer base. Having an in-house support staff, in my mind is far preferable to outsourcing this important day to day link with customers.