Should you just take their word for it
No, a general rule of thumb is not to believe anything unsupported a stranger tells you when the outcome of convincing you benefits their agenda. This holds true whether it's someone in a van offering you a lollipop while you're walking home from school, or a potential client wanting some reverse engineering done. A judgement call needs to be made based on what they're trying to convince you to do. But don't assume honesty straight away.
should you make provision for checking if they're being honest about it or not.
Yes, you should do what you can, either that or just decline the job. You may not get definitive information, but if you find enough to allay your suspicions, that's all that's needed. This isn't about legality. One way is to check on the company and the person doing the requesting. I have found that a bit of time on google and looking at websites usually gives me enough information to make a 'gut' judgement call.
Eg,. it might be a solid looking company who have had the app for quite a while, but you can't find any connection between the person requesting the job and the company. Or worse still you find a connection but the person no longer works there.