First, be careful. I wouldn't hack or hijack a remote control unless I had or was sure I could obtain a replacement unit. If nothing else, Murphy's Law might mean you would have less probability of breaking it as you experimented.
Ring is positive
is not proof they are all
connected to Vdd
the OP could be reading pulled high rings?
What are the dots measuring?
Are these button switches never a scanned matrix in this kind of remote?
Low(er) knowledge solutions:
Use a small relay for each switch you want to press. That's isolated tots and lets one "press" the button by operating the NO contacts on the relay.
Or
Use a CMOS switch, like in a 4066, just like you would have done with the relay. Power the CMOS IC with the remote Vdd/Vss, common ground to the Arduino and deal with the logic level translation necessary to close the CMOS switch using an Arduino output signal.
I never tried the CMOS thing. Just now I cannot google up anyone who has, but always had in mind to research or just try it as it seems entirely plausible.
I look forward to the heavies' opinions on the CMOS idea.
Both methods should work no matter the real switches pull high, low or are matrix scanned.
One problem with of all methods, to varying degrees, is the mechanical concept; seems unlikely that you could end up with something yet handheld w/o some clever cramming it all in there... obvsly relays are out if that is a desired goal.
BTW I feel there is enough "reverse engineering" in doing this that the OP would def qualify for the merit badge, at least the first level. 
HTH
a7