Oh dear! you appear to have got yourself all worked up over nothing
Just make sure you are clear on why you want this one!
If it bothers you that much either a- lie and say you applied to other posts or B- quickly apply to some and then say you've applied
I don't see what difference it makes, they are not assessing your ability to apply for PhDs, they'll be trying to figure out if you are the right person for the job and thus get the funding - so focus on why you are the only person they should consider.
And if they ask you if you've applied to others you could say, you are being very selective and only applying to PhDs that particularly interest you, then tell them your interests etc etc
good luck
S