Several reasons:

1. Tomatoes have a high acidity, but many other foods (I mean, wine, for crying out loud! From ubiquitous pewter glasses!) would have had a higher acidity. Vinegar was commonly used in a variety of dishes.

2. Lead poisoning is not usually a sudden event that causes you to say "My god! Must have been the tomatoes!" If there even was a connection, it would have taken a large scale analysis that would have more strongly identified that "people who eat off of pewter tend to get these symptoms." After all, it wasn't just the wealthy eating tomatoes. It just makes no sense that they could have linked the two, especially after all of the incredibly blatant health hazards that hadn't been linked together.

3. Tomatoes are clearly a member of the nightshade family, and this was known in the 1700's. Although lots of great things come from the family (chili peppers, tobacco!) they're often not things to mess with, and might kill you. Potatoes also had a similarly bad reputation because of this. An over-cautious biologist and a little misinformation (or perhaps an early variety of tomato with too much solanine or something nasty in its leaves) seems a lot more likely than "lead poisoning"

4. The source that was linked to for this "fact" is a book on growing Heirloom tomatoes that has nothing to back this up at all, and is far from a "scholarly resource" Seems like a lot of irresponsible reporting.