This may sound petty, without another ground connecting the two you are depending on the braid of the coax as your ground...
Well, yes and no.
You are relying on the coax shield to provide the ground side of the RF transmission
line between the rig and the tuner, of course. But if that opens, having a second
path between them doesn't really help - it is better to fix the coax. That isn't the
reason you would connect the ground lugs together.
Before you can go any further you have to decide why
you want to bond
the rig ground to the tuner ground in the first place. Bonding makes no difference
if there isn't a voltage difference (RF or DC) between them that causes problems.
And, most of the time, the answer is, " because it is ham radio lore
", a byproduct
of times when people didn't understand common mode currents and the like, and
found that, sometimes, such problems could be reduced by adding a ground, even
if the ground was totally ineffective. (Most ham station ground leads are far too
long to provide an effective ground, particularly on the higher HF bands.) Of course,
sometimes such grounds would make the problem worse, but if you only add them
when you have a problem in the first place you won't notice that.
I've been using antenna tuners since I built my first "Ultimate Transmatch" on a
sheet of perforated Masonite over 40 years ago, and I can't remember ever
worrying about bonding the tuner ground to the ground lug on the rig. There
have been times when I used the bonding post to attach radials to the tuner,
or even a wire to a ground stake when static build-up caused the variable
capacitors to arc. Occasionally I've added radials to the ground lug on the
rig to solve RF-in-the-shack problems. But I've never encountered a situation
where bonding the tuner to the rig would make any difference.
Not that there might not be such a situation at some point. But until someone
can explain why there is a voltage differential between the two units, including
where the current is coming from and where it is going, in a way that doesn't
have an Electrical Engineer spewing coffee on his keyboard when he reads it,
just get on with the business of making contacts and don't worry about it.