I remember at the shop where I got the SunPulse lamps and Nanolux ballast, the people there warned me not to touch the lamps with bare hands, as the finger oils will mess it up. Is this true?

Yes, many lamps could be damaged by the finger prints. It is the case for practically all hot running bulbs like halogen capsules, small outer size or bare tube HID's and so on.
The fingerprints tend to "attach" dirt, so forming spots with worse cooling and absorbing more radiation (and converting that to heat). That means these spots tends to really overheat, it is quite common to see failed instrumental halogens with a bubble featuring a finger print...
Plus the remains of the heat dissociated oils tend to be chemically aggressive towards the quartz and glass.
In any case these oils do create quite visible brownish stains even on standard incandescents (although these usually survive that without other problems).
So it is generally advisable to not touch the lamps with bare hands and/or after that wipe them clean. The more sensitive hotter running bulbs will need more thorough cleaning with some alcohol or so...

The bulbs in question are tubular shaped 400 Watt MH bulbs, and they have an outer envelope.

This is only true with halogen lamps, where the quartz outer heats to very high temperatures, enough to cause the oil from your fingers to weak the quartz. You can touch your 400W MH lamp without problem, it outer is made from hard glass and runs much cooler than the quartz outer of a halogen lamp, and can be handled like an incandescent lamp.

The touching of lamps with bare hands-this applies to lamps that are quartz outer envelopes-glass should be OK.High pressure Xenon bulbs used for cinema projectors often have an alcohol wipe with them so the bulb can be wiped off after installation in the projector lamphouse-you are supposed to wear gloves anyway as well as a ballistic jacket and facemask if the bulb blows during installation or removal of the old bulb.This rule(barehand rules) also applies to quartz halogen bulbs in slide and overhead projectors,and even quartz car headlight bulbs.

With halogens it applies to the hard glass capsules as well.

For the colder running bulbs (most outer jackets,...) it is indeed not directly damaging them, but still in that heat it forms the stains. So it is better to keep even these clean, if ever possible (using clean gloves,...).
Of course, it depends how oily/sweaty your hands use to be, when someone has them really dry, it won't cause anything, but I really have to wipe everything I touch...

The higher power tubular HIDs do reach temperatures where this may be a problem. The extreme of that was when some tubular shape 400W MH's had the outer bulb "suck in" around the arctube, that is when they started to come up with shapes like the "Bulged Tubular" (not the Mercury-like BT, the other one with the small bulge). My practice is to screw the lamp in with the box, then take off the box

The problem is not the glass being damaged by the fingerprints, it just becomes dirty...

Not good either

But in some 400W tubular lamps there really is problem with the outer glass, it would soften near the arctube and "suck in" when burning horizontally

Not good either

But in some 400W tubular lamps there really is problem with the outer glass, it would soften near the arctube and "suck in" when burning horizontally

Sounds like I should be keeping my MH lamps squeaky clean.

Sounds like I should be keeping my MH lamps squeaky clean.

Well, that never hurts...

I think there is no problem touching the outerbulb of screwbase MH and HPS lamp. I even touch my RX7s compact double enede MH lamps with bare hands (They didn't came with a glove for handling, like halogens), and they are still OK.

Touching the double ended lamps i'd say is allready real bad. For the big envelopes its not much of problem except possibly the 400W MH. but still better not to

Also, its bad practice to leave fingerprints on Aluminum reflectors in the luminaire

We need a real answer now. Too many different opinions to come to a conclusion.

We need a real answer now. Too many different opinions to come to a conclusion.

And what if no conclusive answer exist?