'Most of the time, its an offer not made for your strengths, but in sympathy, giving you a way out. '
I don't think a company ever acquires another company because they feel bad. If they want to buy you it means that your company could play an integral part of their strategy. If it seems like they think they're doing you a favor then that means they are trying to low-ball you and you should ask for a higher price.
This is essentially substance-free pabulum that makes a wild over-generalization based on a small handful of anecdotes from the 90s.
Yes, if you limit your dataset to "every great startup," then, yes -- you should go back in time and bet on them when they're still an underdog. Whatever that means. Go back and bet on Google. Become employee #1 at Facebook. Buy 10% of Twitter in 2006.
How many times has someone bet on the underdog and lost? I'm not really comfortable with OP choose the evidence they like in this way. Where's the basis for comparison? If you're talking of betting, how are you defining the reference class and what are the odds?
I don't think a company ever acquires another company because they feel bad. If they want to buy you it means that your company could play an integral part of their strategy. If it seems like they think they're doing you a favor then that means they are trying to low-ball you and you should ask for a higher price.