So, if all goes well, which with me it usually doesn't, but if it does then I'll be joining a new group sometime in the next couple of weeks. Unfortunately, they use a very limited set of rules and have a basic agreement that you can only use it if you own it.
This conflicts with me on several levels.
For one thing, I utterly refuse to buy hard copies of 4e materials. I will subscribe to DDI and that will be my sole source of 4e material.
A DDI sub should cover you for the "you can only use it if you own it" part of their rules.
As for the limits as to the available ruleset, that shouldn't be a problem - get the DM to give you a list of available sources, and set up your Character Builder to only show options from those sources. Done.
Now, there may be a problem if you're not willing to accept their limitations on which books to use, in which case I would say you either need to accept their rule or leave the group. If you expect them to open the game up to everything just to suit you, then I'm afraid you're the one being unreasonable.
There may also be a potential problem if they insist on using the old books "as published" (that is, no errata), and
especially if they won't accept that your character is "close enough". (Potentially, the problem also exists if they
don't accept the DDI as being enough for "you own it"...)
In this case, I would say that they're probably being unreasonable. Still, the reality is that your choices remain: accept their rules, or leave the group.
As far as persuading them around to your point of view (that they should play using the latest errata, that the DDI is definitive, and that they should play "anything goes"), that's down to tact and diplomacy, same as anything else.