I have heard that before, and it is likely because of the same reason Pakistan was always pro US, dating back to Cold war period. US backed the Islamist movements across the globe at the time, as it was effective to countering communism.
Jamaat 's leaning towards US is one of the reasons their politics is not held in high regard by pro Khilafah or traditional Islamic minded individuals and parties in BD. In addition to the fact that they follow the democratic system. Even Islami Andolon (Charmonai Pir's Party) had a breakdown in talks for alliance with Jamaat recently, although that was perhaps for a different reason.
Nonetheless, a strong Jamaat and in essence a coalition of Islamic parties, whether in power or effective primary opposition, remains the best option to countering an Indian government with hegemonic agenda in my opinion. This is because, behind the intrusive and imperialist approach of Indian governments - revenge for hundreds of years under Muslim rule and a return to pre Islamic "Akhand Bharat" is a key motivator for many within Indian government. It was always about religion. You are obviously more well read on this matter than I am.
At least BJP govt is open about it with their approach regarding Muslims.
Which is why I will disagree on the point that religious beliefs aren't sufficient to counter Indian or any other foreign aggression. It mostly is, but you will always have a bad apple here and there. No system is ever bulletproof. Just like Hezbollah had the Cellphone attacks and Nasrallah death - which are certainly because of traitors within. Nonetheless, the jeal you see in Hezbollah and Hamas combatants has almost everything to do with religious belief. Compare the stature of Hamas with that of Fatah now. One is growing in numbers while the other is being called out as Zionist puppet. The difference being - Hamas is driven by religious ideology, while Fatah follows secular nationalism. Religion does play a huge role in an individual's psyche.
From my personal interactions with Shibir members, religion plays a huge role in their life and that keeps them well directed towards their objective. I am generalizing but they have a fear of afterlife - which keeps them in check. That's why we saw so many undercover Shibir members exposing the Chatro League secret WhatsApp groups and discussions by infiltrating their ranks. Without religion acting as the moral compass, it would have been much easier for them to just assimilate, maintain status quo by keeping Hasina in power and make a fortune through all the criminal activities Chatro League used to conduct.