Agree! When you apply "arm bar" on your opponent and your legs are across your opponent's body, you will give him a chance to bite you. The reason is simple. Your opponent will still have a "free arm" that can pull your leg toward his mouth.
Here are examples:
Sorry it took me a while to get to this. I only have a few training partners who I know are willing to do experiments like this and I had to wait until I had a chance to work with one of them.
For my experiments I got a friend who is a purple belt in BJJ (as well as a black belt in Karate, instructor rank in Muay Thai, and plenty of real-world experience with violence). We tested out the Juji-Gatame armbar both from the top and from the bottom of guard.
First test: we started with me on top having already secured the arm bar control position, but not having the arm extended yet (is arm was still bent at 90 degrees. We determined that if I had my preferred control position locked in firmly, he could barely reach my leg with his teeth, but with a bit of straining he could just barely get his teeth into a bit of flesh. I let him go ahead and get the best bite he could manage, then we started with me slowly extending his arm and him doing his best to gnaw on my leg.
Result: I felt like he wasn't able to get a deep enough bite threaten more than the skin, and with the pants in the way I didn't feel like he would even be able to break the skin. The discomfort was no more than a mild annoyance as I slowly extended his arm and got the tap. (Of course, in a real fight I would have snapped the arm in an instant.)
Second test: we started with me on top in the arm bar control position, but with him already defending the arm bar by clasping his hands, which would him more time to work his bite, since I couldn't finish the arm bar without first breaking his grip. Once again I allowed him to get the best mouthful of my flesh that he could manage before we began.
Result: This time, instead of working to finish the arm bar, I placed a thumb over one of his eyes (which were beautifully aligned to be targets), and very slowly pressed until he let go the bite. He couldn't defend using his hands without exposing himself to the arm bar and he couldn't move his head to escape without letting go of his bite. Once again, I felt no real threat to my leg. I was more worried that he would try to resist the eye push for too long. (Once again, in a real fight I wouldn't have been pressing so slowly.)
Third test: once again we started with me in top control position and my partner defending the arm bar using his other hand. This time, however, we had my partner take Kung Fu Wang's suggestion and also use his "free hand" to try pushing my leg into a better position to get a good bite.
Result: My partner was able to get a slightly better bite. However by using his free hand to try pushing my legs he weakened its defense of the endangered arm and I was easily able to break his grip, extend his arm and get the tap. Even though his bite was slightly better, it still didn't hurt enough for me to worry about it. (I should also note that since many arm bar escapes work by pushing a leg out of position, a good arm bar artist knows how to lock their legs into position where it is very difficult to move them at all.)
Fourth test: We started with me in an ideal arm bar control position from guard, with his arm not extended yet.
Result: My partner was completely unable to bite me at all, because I had his head position controlled so he couldn't turn towards my legs.
Fifth test: We started in a less ideal arm bar control position from guard, where he had good enough posture so that he could reach my leg for a bite, and also allowed him to connect his hands for an attempt at defending the arm bar.
Result: My partner was able to get a weak bite before tapping as I slowly extended his arm.
Sixth test: We started with an already compromised arm bar attempt from guard, with my partner having me stacked and his arms in a solid defensive position, so that he would have plenty of time to work his biting.
Result: Just as I would in a non-biting context, I immediately abandoned the arm bar attempt, because I don't want to be stacked or get slammed, or waste my energy on a submission which isn't set up properly.
Final tests: we repeated all of the above, except now my partner was applying the arm bar and I was biting.
Result: Since my training partner is a purple belt, his arm bar control positions were not as tight as mine. I felt like I was able to get slightly deeper bites on him than he could get on me. He said that they still didn't feel that threatening or painful and he was still able to work on extending the arm bars. However, he did react to the bites more than I did - not letting them go, but shifting his legs momentarily or pushing on my head to make me let go. This sometimes gave me just enough of an opening to use some of my standard arm bar escapes to get out. To be clear, he didn't let go of the arm bar and I wasn't inflicting any significant damage with my bites - I just induced enough of a flinch reaction to give me an opening which I could use because I am a black belt and he's a purple belt. Of course, for that same reason I might have been able to escape the arm bars anyway, but I'd say it made things about 10% easier. I would still probably not use this tactic in a real street fight because anyone who could manage to catch me in an arm bar in a real fight is probably either a professional fighter or another BJJ black belt or the equivalent level in another grappling art. If I tried biting someone like that and it didn't work, they would probably break my arm and then be mad enough to continue on with some additional body parts.
All this was actually pretty close to my expectations. I actually thought my partner might be able to get a deeper bite to start with. As it turned out, I really didn't feel any threat from the bites even if I wasn't able to complete the arm bars. This is part of why controlling position is so important. I always tell my students that every submission is a control position first. (BTW - the arm bars illustrated in the pictures from KFW's post are all somewhat flawed from my perspective.)
Thanks to Kung Fu Wang for raising an interesting question for the BJJ research labs!